Preheat oven to 350°F. Line 8-inch square baking pan with parchment paper. Allow parchment paper to run up the sides of the pan to help with unmolding. Lightly grease parchment with butter or cooking spray. Set aside.
CAKE: In the bowl of a stand mixer, using a paddle attachment cream together butter and sugar until smooth. Add eggs and vanilla. Mix until well combined. Scrape down sides of bowl as needed.
In another bowl, whisk together flour, baking powder, baking soda, and salt. Add half of dry flour mixture to mixing bowl. Mix on low speed. Add milk. Mix on low speed until incorporated. Follow up with remaining flour and mix on low speed until there are no longer any dry streaks of flour. Scrape down sides of bowl to ensure thorough mixing. *Batter will be thick.
PLUMCOT: Toss sliced plumcots in sugar. Set aside.
CRUMB TOPPING: Whisk together flour, sugar, cinnamon, and salt. Use a pastry cutter or two forks to cut cold butter into dry ingredients until mixture resembles coarse sand. Alternatively, use a food processor to roughly pulse ingredients together. Set aside.
ASSEMBLY: Spread 2/3 of cake batter into prepared baking pan. Arrange sliced plumcots on top, including any expelled juices. Dollop remaining 1/3 batter on top of fruit. Spread batter into an even layer. Sprinkle crumb topping all over surface.
Bake for 38-40 minutes until toothpick inserted in center of cake comes out clean. Rotate pan midway through baking to ensure even cooking. Allow cake to cool in pan for 20 minutes before unmolding. Remove from pan and cool to room temperature on wire rack.
Use a serrated knife and slice cooled cake in a gentle sawing motion. If desired, dust with sifted powdered sugar before serving.