Preheat your oven to 375°F and grease a 9x9-inch baking dish or a similar-sized dish.
In a large bowl, mix the frozen mixed berries with granulated sugar, cornstarch, lemon juice, lemon zest, and vanilla extract until evenly coated. Pour the berry mixture into the prepared baking dish and spread it out evenly.
5 cups frozen mixed berries, ¼ cup granulated sugar, 2 tablespoons cornstarch, 1 tablespoon lemon juice, zest of half a lemon, 1 teaspoon vanilla extract
For the topping, whisk together the flour, granulated sugar, brown sugar, baking powder, and salt in a medium bowl. Add in the melted butter, and vanilla extract and mix until the mixture resembles cookie dough.
1 cup all-purpose flour, ½ cup granulated sugar, ¼ cup brown sugar, ¾ teaspoon baking powder, ¼ teaspoon salt, ½ cup unsalted butter, ½ teaspoon vanilla extract
Sprinkle the cookie dough streusel topping evenly over the berry filling. Bake in the preheated oven for 40-45 minutes, or until the topping is golden brown and the berry filling is bubbling around the edges.
Allow the cobbler to cool for at least 10 minutes before serving. Serve warm, optionally with a scoop of vanilla ice cream or a dollop of whipped cream.