Butter and flour a 9-inch-across, 3-inch-deep springform pan. In a large sauté pan, melt 3 tablespoons of the butter, then sauté the apples over medium-high heat until softened and browned in spots, about 5 minutes. Mix 3 tablespoons of the white sugar and the cinnamon’ in a cup and sprinkle over the apples, then toss and cook until the liquids are thick and bubbly.
Preheat the oven to 350°F.
Dice the remaining ½ cup of butter, and let it come to room temperature. In a stand mixer, combine the flour, brown sugar, and salt, and mix. Toss in the diced butter and mix until the butter is broken into small bits. Measure 2/3 cup of the mixture into a small bowl, and stir into that the remaining 2 tablespoons white sugar and pie spice to make the streusel.
To the mixer, add the baking soda and mix, then add the pumpkin, sour cream, and eggs, beating until smooth. Scrape the batter into the prepared pan.
Distribute the apple sauté over the batter, then sprinkle the streusel topping over that.
Bake for 40 to 50 minutes, until a skewer inserted into the center of the cake comes out clean. Cool on a rack.