Preheat the oven to 350˚F. Grease an 8-inch square baking pan with some butter, and line the bottom with parchment paper, leaving an overhang on two sides. Butter the parchment paper.
In a medium bowl, whisk 3/4 cup of the flour with the baking powder and salt. Using a standing mixer, beat the butter and coconut oil together until fluffy with the paddle attachment, about 3 - 5 minutes. Add the sugars and the vanilla extract, and continue to beat until completely incorporated into the butter.
Add one egg at a time, beating well after each addition. Fold in the dry ingredients all at once using a spatula. Work the batter only until the flour in completely mixed into the batter.
Spread the batter evenly in the prepared pan and lightly top with the lemon curd. Sprinkle with the blueberries and peach slivers. Finish with the Crumb Topping (recipe below).
Bake until golden and a toothpick inserted in center comes out with moist crumbs attached, 40 to 45 minutes. Cool in pan for 15 minutes and pull out using the paper overhang. Cool completely and cut into squares.