Amish Baked Oatmeal

large eggs 1/2 cup packed brown sugar 1/2 tablespoon baking powder 1/2 tablespoon vanilla 1 teaspoon cinnamon 1/4 teaspoon kosher salt 1/4 cup butter, melted 1 1/4 cups milk (regular, almond, etc.–choose your favorite) 3 cups old-fashioned rolled oats