Preheat oven to 375°F. Spray a 12-cup muffin tin with baking spray or grease with butter and flour.
In a medium bowl, sift together 2 cups flour, baking powder, salt, and 2 teaspoons cinnamon. Set aside.
In a small bowl, mix 2 teaspoons flour with ½ teaspoon cinnamon. Add diced apples and toss until lightly coated. Set aside.
In a large mixing bowl, beat room temperature butter and 1 cup sugar together for 3 minutes until light and fluffy.
Add eggs one at a time, mixing well after each addition. Stir in vanilla extract.
Add flour mixture in three parts, alternating with milk (flour, milk, flour, milk, flour). Mix just until combined. Don't overmix - small lumps are fine.
Gently fold in the cinnamon-coated apple pieces using a spatula with large sweeping motions from bottom to top.
Scoop batter into prepared muffin cups, filling each about two-thirds to three-quarters full.
Bake for 30 minutes, or until a toothpick inserted in the center comes out clean or with just a few moist crumbs.
While muffins bake, melt ½ cup butter for topping and let cool slightly. Mix ¼ cup sugar and ¼ cup cinnamon in a shallow bowl.
Remove muffins from oven and let rest for 5 minutes. Remove each muffin, brush the top with melted butter, and roll in cinnamon sugar mixture.