In a large bowl, whisk the eggs until frothy. Add the flour, sugar, baking powder, baking soda, salt, buttermilk, melted butter, and vanilla. Stir just until the batter is smooth and no lumps remain; do not overmix. Using a rubber spatula, gently fold in the blueberries. Set a large nonstick frying pan or griddle over medium heat and let the pan heat for about 2 minutes. Add 2 teaspoons butter to the pan and use a silicone spatula to spread it evenly over the surface.