In a medium bowl, combine all the crumble topping ingredients—flour, brown sugar, butter, and pumpkin spice—using a fork or pastry cutter until the mixture is coarse.

In a large mixing bowl, whisk together 2 cups of all-purpose flour, 1 teaspoon of baking powder, ½ teaspoon of salt, and 2 teaspoons of pumpkin spice.

In another bowl, whisk 3 eggs until fluffy, then add in 1 cup of sugar, ½ cup of softened butter, 1 cup of sour cream, 1 cup of pumpkin puree, and 2 teaspoons of vanilla extract. Mix until smooth.

Gently blend half of the dry mixture with the wet ingredients, mixing just until incorporated. Add the remaining dry ingredients and fold until no flour streaks remain.

In a medium bowl, beat together 8 ounces of cream cheese, ½ cup of powdered sugar, and 1 egg until smooth.

Preheat your oven to 350°F (175°C). Grease a springform pan and pour half of the cake batter into the pan. Spread the cream cheese filling, then pour the remaining batter on top.

Place the cake in the preheated oven and bake for 40-45 minutes, or until a toothpick comes out clean.

Let the cake cool in the pan for about 10 minutes before transferring it to a wire rack to cool completely.