Topping: Preheat oven to 350 degrees. Whisk together flour, brown sugar, and salt in a small bowl. Stir in butter until combined.
Cake: Brush a 9-by-9-by-2-inch square cake pan (not nonstick) with butter. Line with parchment, leaving a 2-inch overhang on two sides; butter parchment.
Whisk together flour, baking powder, and salt in a medium bowl. In another bowl, beat butter with granulated sugar on medium-high speed until light and fluffy, about 2 minutes. Add eggs, one at a time, beating to combine after each. Reduce speed to low and add flour mixture in 3 batches, alternating with 2 additions of milk, beating until combined and scraping down bowl as necessary.
Transfer batter to prepared pan. Spread jam evenly over top. Sprinkle evenly with topping, squeezing to create large clumps. Bake until a tester inserted in center comes out clean, 45 to 50 minutes. Let cool in pan on a wire rack 20 minutes. Use parchment to lift cake out of pan, then let cool completely on rack before serving.