Preheat your oven to 350°F (175°C) and melt 4 tablespoons of unsalted butter in a 9 x 13-inch baking dish.

In a medium saucepan, melt 1/2 cup of unsalted butter and cook until it turns a caramel color, stirring frequently.

In a medium bowl, combine 2 cups of fresh blueberries with 1/4 cup granulated sugar and lemon zest, then set aside.

Whisk together 1 1/2 cups of all-purpose flour, 2 teaspoons of baking powder, and a pinch of salt in a large mixing bowl. Add sugar, milk, browned butter, and vanilla extract. Mix until smooth.

Pour the batter into the baking dish, then spoon the blueberry mixture on top, distributing evenly.

Sprinkle 2 tablespoons of granulated sugar over the top and bake for 45 to 50 minutes until golden brown.

Allow the cobbler to cool for about 30 minutes before serving it warm with ice cream.