In a food processor fitted with an S-shaped blade (the standard blade), add the flour, brown sugar, remaining granulated sugar, baking powder, and salt. Pulse a few times to combine all ingredients.
Add the cold, cubed butter to the food processor and pulse a few times until mixture starts to come together but is still sandy.
Add the egg yolk and the vanilla extract, and pulse again to combine until all ingredients are mixed together. This mixture should still be a little crumbly, a little like pie dough before it all comes together into one ball.
Scoop out a 1/2 cup of the dough into a small bowl and set in the fridge.
Tip the rest of the dough into the prepared baking pan. Use your fingers to press the dough firmly and evenly into the pan, pressing it up about 1/4 inch around the edges of the pan.
Smooth the apple butter over the dough until the surface is evenly covered.
Crumble the remaining 1/2 cup of refrigerated dough over the apple butter; it's okay if the apple butter is mostly covered.
Sprinkle the top of the bars with the cinnamon sugar mixture, then place baking pan in a 375F oven and bake until golden brown, about 35 minutes.
Remove the pan with the baked bars to a wire cooling rack, and let the bars cool completely before cutting and serving.**