Preheat the oven to 350°F.
Place the 2 tablespoons of unsalted butter in a 9 × 13-inch casserole dish. Transfer the dish to the warming oven and allow the butter to melt, which should require only a few minutes. Watch it carefully so the butter does not burn.
Meanwhile, melt the remaining ¼ cup of unsalted butter in the microwave without overheating it. Set it aside briefly so it can cool slightly before being incorporated into the batter.
Add the 2 cups of all-purpose flour, baking powder, baking soda, salt, and granulated sugar to a large mixing bowl.
Whisk thoroughly until the dry ingredients are evenly distributed.
Pour the slightly cooled melted butter, milk, egg, and vanilla extract into the center.
Whisk the ingredients together until a smooth batter forms and no visible lumps remain.
While the butter in the casserole dish is melting, gently toss the blueberries with 1 teaspoon of all-purpose flour until the fruit is lightly and evenly coated. This coating helps the berries remain more evenly dispersed in the batter.
Carefully take the casserole dish out of the oven once the butter has melted.
Using a pastry brush, distribute the melted butter across the entire bottom and along the sides of the dish to reduce sticking.
Pour the prepared pancake batter into the buttered casserole dish.
Scatter the flour-coated blueberries evenly across the surface of the batter.
Return the casserole to the preheated oven and bake for 30 minutes, or until the surface is golden brown and a toothpick inserted into the center comes out clean.
Remove the baked pancake casserole from the oven.
If desired, lightly dust the surface with powdered sugar for additional sweetness.
Slice the casserole into smaller portions and serve with your preferred syrup.