Prepare the souffle molds:
Melt 3 tablespoons of the butter and generously grease your souffle ramekins. Refrigerate the buttered ramekins and then butter them again. Dust the insides of the ramekins with 3 tablespoons of the sugar and return them to the refrigerator. Keep the remaining butter at room temperature.
Make the pumpkin pastry cream:
In a heavy-bottomed saucepan, bring the maple syrup to a boil and reduce it by almost half. A thermometer inserted in the maple syrup should read 140°F when the syrup is fully reduced. Remove the syrup from the heat and allow it to cool in the pan for 10 minutes.
Add the pumpkin puree, half-and-half, and all the spices including the salt to the pan with the maple syrup. Heat the mixture on low, stirring with a whisk, until the maple syrup softens and incorporates into the pumpkin mixture.
Meanwhile, separate the 7 eggs, reserving the whites in the bowl of a stand mixer. Place 4 egg yolks in a medium bowl, reserve 2 egg yolks in a small glass to hold for later, and either discard the remaining yolk or use it for something else. Whisk 2 tablespoons of the warm pumpkin mixture into the egg yolks, and then briskly whisk in the flour, making sure that the mixture is smooth with no lumps or streaks of white, 2 to 3 minutes. While continually whisking, add about half of the remaining hot pumpkin mixture to the egg yolk mixture to warm it, then whisk the egg yolk mixture into the remaining pumpkin mixture in the pan.
Bring the custard to a boil over mediumhigh heat, whisking continuously and making sure to scrape the bottom of the entire pan.
Once the mixture boils for 20 seconds and thickens, remove it from the heat and stir in the remaining 1 tablespoon of butter. Transfer the custard to a clean stainless-steel bowl and allow the mixture to cool.
Make the meringue (see the Note on acid in egg white foams):
Combine all but 2 tablespoons of the remaining sugar and 4 tablespoons water in a small saucepan over medium heat and attach a candy thermometer to the side of the pan. Simultaneously place the 7 egg whites in the bowl of a stand mixer and whisk on medium high speed. Once the egg whites begin to foam up, add the cream of tartar.
When the egg whites are completely foamy and begin to hold the lines of a whisk, turn the heat under the pan of sugar syrup to high. Once the sugar syrup has come to a rolling boil and reaches 225°F to 230°F, gradually add the remaining 2 tablespoons of sugar, 1 teaspoon at a time, to the egg whites. As you add the sugar, the whites should become shiny and gain volume. If you see the whites beading (small lumps of egg whites forming on the side of the bowl), you have whipped them too dry; slow the machine down and add the remaining sugar.
Once the sugar syrup on the stove reaches 248°F quickly, in a slow continuous stream, pour the hot syrup into the egg whites with the mixer set on a medium-high speed. The whites should still gain more volume and take on a satiny white color. Continue to whip the meringue on medium-high speed until it stiffens and cools, 3 to 5 minutes.
Fold the meringue into the pastry cream (see "Raw egg yolks in pastry cream for souffle" in the Notes section, below):
Once the meringue is done, whisk the remaining 2 egg yolks into the pumpkin pastry cream. Add about a quarter of the meringue to the pumpkin custard to lighten it and then add the remaining meringue. Place a spatula in the center of the bowl, scrape the bottom, and bring the bottom over the top. Rotate the bowl 45 degrees and continue folding until all the egg whites are incorporated.
Fill the prepared ramekins:
Using a rubber or plastic spatula, fill the prepared ramekins with the mousse, avoiding leaving any air pockets under the mousse in the ramekins. Flatten the tops of the ramekins with a metal spatula, scraping any excess mousse back into the bowl. Clean off any bits of mousse that might have dripped onto the sides of the ramekins.
Bake the souffle:
You can now either bake your souffles or place them in the refrigerator, covered, for up to 4 hours or in the freezer for up to 24 hours. Before baking frozen souffles, allow them to sit out at room temperature for 1` hour. When you are ready to bake the souffles, preheat the oven to 375°F. Bake the souffles until they rise over the rims by about ½ their original volume, 9 to 12 minutes in a convection oven or 15 to 20 minutes in a regular oven without a fan.
Serve these souffles as soon as they come out of the oven. I recommend serving this souffle with Maple-Ginger Ice Cream and crispy Gingersnaps. You can also serve it with vanilla ice cream and a plain wafer. Caramel or cinnamon ice cream makes a nice accompaniment. Or pass around a small bowl of whipped crème fraîche or cream for guests to dollop on top of their souffles after they have taken that first aerated spoonful.