Combine flour, sugar, baking powder, and salt in a bowl. Cut in butter using a pastry cutter or your hands until coarse crumbs form.

Whisk milk, egg, and vanilla extract together in a small bowl. Add to flour mixture and knead until just combined, adding a little more flour if too wet or a little more milk if too dry. Divide the dough into thirds; 2/3 will be for the bottom, save 1/3 for the top.

Roll 2/3 the dough out onto a lightly floured surface into an 11x15-inch rectangle. Place dough into the bottom of a 9x13-inch baking pan, making sure it comes at least halfway up the sides.

Combine pineapple and sugar in a small saucepan and bring to a boil over medium heat, about 5 minutes. Meanwhile, pour reserved pineapple juice into a bowl and add cornstarch; stir until dissolved. Add to the saucepan and stir until thickened, about 5 minutes more. Remove from heat and let filling cool in the refrigerator, about 15 minutes.

Scrape filling onto the bottom dough in the baking pan and smooth out.

Preheat the oven to 350 degrees F (175 degrees C).

Roll remaining 1/3 dough out onto a lightly floured surface into a 9x13-inch rectangle. Roll the dough onto the rolling pin and unroll on top of the pineapple filling, making sure edges of the dough reach the edges of the pan.

Combine flour and sugar in a small bowl. Add vanilla extract and cut in butter until coarse crumbs form. Sprinkle streusel topping over dough.

Bake in the preheated oven for 45 minutes. Remove from oven and let cool on a rack. Cut into 24 squares.