Step 1
Heat oven to 350 degrees. Line a 9-inch square baking pan with parchment paper, leaving a 2-inch overhang at each side. Brown the butter for the cake: Melt butter in a small saucepan over medium heat, cooking just it until brown spots appear, 6 to 8 minutes. Set aside to cool.
Step 2
Make the crumble: In a medium bowl, mix together 1 cup/128 grams flour and 1 cup/220 grams light brown sugar. Add the cold, cubed butter. Using your hands or a pastry cutter, work the butter into the flour and sugar until combined. (The mixture will have the consistency of wet sand.) Using your hands, pinch and press the dough together, making the crumbs as small or large as you’d like. Set aside.
Step 3
Prepare the cake: To a large bowl, add the browned butter, ¾ packed cup/164 grams brown sugar, ½ cup/100 grams granulated sugar and the vanilla and whisk to combine. Whisk in eggs one at a time until light and creamy.
Step 4
In a second bowl, combine 2 cups/256 grams flour, the baking powder, baking soda and salt. Alternate adding the dry ingredients and the buttermilk a little at a time to the egg-sugar mixture, stirring with a spatula until incorporated.
Step 5
In the now-empty flour bowl, combine the remaining 2 tablespoons flour and 2 tablespoons brown sugar. Add the peaches and toss until evenly coated. Fold the peaches into the batter, and spread batter evenly into the prepared pan. Top with the crumble.
Step 6
Bake until the topping is lightly golden and a toothpick inserted into the center comes out clean, 40 to 50 minutes. Let cool in the pan on a wire rack. (If you’d like, use the parchment overhang to lift the cake out of the pan before cutting into pieces.)
Step 7
As the cake cools, prepare the glaze, if you like: Mix together powdered sugar and 2 tablespoons maple syrup – add more to get to your desired consistency – and drizzle on top of the cooled cake.