01 - Preheat the oven to 375°F. Lightly butter a 9-inch baking dish and set aside.
02 - In a large bowl, combine the mixed berries, ⅔ cup granulated sugar, cornstarch, lemon juice, vanilla extract, and a pinch of salt. Toss gently until the berries are evenly coated. Transfer the mixture into the prepared baking dish, spreading it into an even layer.
03 - In a separate bowl, whisk together the all-purpose flour, almond flour, ⅓ cup granulated sugar, baking powder, and ¼ teaspoon salt until well blended.
04 - Add the cold cubed butter to the flour mixture. Using a pastry blender or your fingertips, cut the butter into the dry ingredients until the mixture resembles coarse crumbs with some pea-sized pieces remaining.
05 - In a small measuring cup, stir together the whole milk, vanilla extract, and almond extract. Pour the liquid into the flour-butter mixture and stir gently just until the dough comes together. Be careful not to overmix.
06 - Drop spoonfuls of the cobbler dough over the berry filling, covering most of the surface. Leave a few small gaps to allow the berries to bubble through during baking. Sprinkle the sliced almonds and coarse sugar evenly over the top.
07 - Bake on the center rack for 35 to 40 minutes, or until the topping is deeply golden and the berry filling is bubbling around the edges.
08 - Remove from the oven and allow the cobbler to cool for at least 15 minutes before serving. Serve warm, optionally accompanied by vanilla ice cream or fresh whipped cream.