To make the dough:
Stir together 2 cups (9 ounces/255 grams) of the flour, the sugar, yeast, salt, cardamom, nutmeg, and cinnamon in the bowl of a stand mixer; set aside. In a small, heavy saucepan, combine the milk and butter and heat over low heat just until the butter melts. Add the water and set aside until warm (120 to 130 degrees F), about 1 minute.
Pour the milk mixture over the flour-yeast mixture and mix well with a rubber spatula until all of the dry ingredients are moistened. Attach the bowl to the mixer, and fit the mixer with the paddle attachment. With the mixer on low speed, add the eggs, one at a time, beating after each addition until incorporated. Add the vanilla in the final moments of mixing.
Stop the mixer, add ½ cup (2¼ ounces/65 grams) more flour, and resume mixing on low speed until smooth, 30 to 45 seconds. Add 2 tablespoons additional flour and resume mixing on medium speed until the dough is smooth, still soft, and slightly sticky, about 45 seconds.
Sprinkle the work surface with 1 tablespoon of the flour, and center the dough on the flour. Knead the dough gently until it is smooth and no longer sticky, adding an additional 1 to 2 tablespoons flour only if necessary to prevent stickiness. Place the dough in a large bowl, cover the bowl securely with plastic wrap, and let the dough rise in a warm place (70 degrees F) until doubled in bulk, 45 to 60 minutes.
The dough is ready when a finger gently pressed into it leaves an indentation. Meanwhile, prepare the baking pan, the glaze, and the filling.
To make the Butterscotch Glaze:
Lightly coat a 9 by 2-inch round cake pan with nonstick spray, or butter the pan. Combine the sugar, butter, and corn syrup in a small, heavy saucepan and set over low heat until the butter is completely melted.
Pour the mixture into the prepared pan and tilt the pan to cover the bottom evenly; set aside. (The glaze might thicken slightly before it’s time to place the dough in the pan, but it will liquefy again as the coffee cake bakes.)
To make the Cinnamon-Butter Filling:
In a small bowl or cup, stir the cinnamon into the butter; set aside.
Center a rack in the oven and preheat the oven to 350 degrees F.
To assemble the coffeecake:
Gently deflate the dough. On a lightly floured work surface, roll out the dough into a 16 by 12-inch rectangle. Using a pastry brush, spread the butter-cinnamon mixture evenly over the dough. Cut the dough lengthwise into six 2-inch-wide strips. (A pizza cutter is helpful here.)
Loosely (so the dough has some give as it expands in the oven) roll up 1 strip and place it, cut edge up, in the center of the prepared pan on top of the glaze.
One at a time, coil the remaining dough strips around the center strip, starting each strip at the end of the previous one, to make a single large spiral. As you roll the dough strips around the coffee cake, the butter-cinnamon side of the dough strips should be facing inside. (When you finish forming the spiral there will be plenty of space left in the pan. The spaces around the dough will fill in as the dough bakes.)
Loosely cover the pan with plastic wrap and let the cake rise in a warm place until it is almost doubled in size, about 30 minutes. The dough is ready when a finger gently pressed into it leaves an indentation.
Bake the coffee cake until the top is deep golden brown, about 35 minutes. Check after 20 minutes to make sure the cake is not browning too fast. If it is, cover the top loosely with aluminum foil for the last 10 to 15 minutes of baking to prevent overbrowning. Transfer to a wire rack (if you have used foil, remove it) and let cool for 10 minutes.
Gently tilt the pan and tap the sides on a counter to release the cake sides, then invert a serving plate on top of the cake, and invert the pan and the plate. Leave the pan on the cake for 1 minute, so the glaze transfers to the cake, then gendy lift off the pan. Using a rubber spatula, scrape out any butterscotch syrup remaining in the pan and spread it over the warm surface of the cake.
Serve the cake warm or at room temperature, cut into wedges gently with a serrated knife. This coffee cake is best eaten the day it is baked.