For the crumb topping: Put the flour, brown sugar, apple pie spice and salt in a small bowl and stir to combine. Add the butter and mix thoroughly with your fingers or a fork until all of the butter has been evenly distributed and incorporated into the flour. Form into small to medium clumps with your fingers.
For the cake: Preheat the oven to 350 degrees F. Butter an 8-inch square cake pan.
Whisk together the flour, apple pie spice, baking powder, baking soda and salt in a small bowl.
Beat together the butter and granulated sugar in a large bowl with an electric mixer on medium-high speed until light and fluffy, about 3 minutes. Add the eggs 1 at a time, beating well after each addition. Beat in the vanilla. Reduce the speed to low and add the flour mixture in 3 batches, alternating with the sour cream in 2 additions, beginning and ending with the flour. Beat until just incorporated.
Spoon half of the cake batter (it will be very thick) into the prepared pan and smooth with an offset spatula. Dollop the apple butter on top and carefully smooth with the spatula. Spoon the remaining cake batter on top and smooth the top. Sprinkle on the crumb topping.
Bake until the cake and topping are golden brown and a toothpick inserted into the center of the cake comes out clean, about 1 hour. Let cool in the pan 20 minutes, then invert onto a plate; invert back onto a rack to cool completely.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)