Grease a 9 inch square pan and preheat the oven to 350 degrees. Line a baking sheet with foil. Add the peaches and blackberries to the square pan. Sprinkle with brown sugar, lemon zest, and a squeeze of lemon juice. Toss together.
In an electric mixer, beat together the softened butter and 3/4 cup granulated sugar until they're combined with a sandy texture, about 2 minutes.
Add the flour, baking powder, and salt and beat until crumbly, another minute. Slowly pour in the vanilla and milk and stir until incorporated, then increase the speed and beat until the batter is smooth and fluffy.
Spread the cake batter evenly over the fruit. Sprinkle the remaining 1/4 cup of granulated sugar on top. Slowly pour the boiling water over top, wetting as much of the sugar as you can.
Place the pan on the lined baking sheet and bake for 40-50 minutes or until golden brown. Allow to set up for 10-15 minutes, then serve warm with ice cream.