1. Preheat the oven to 375°F and line a 12-cup muffin pan with paper liners or grease the cups well.

2. In a small bowl, mix 1/2 cup flour, brown sugar, softened butter, and optional coarse sugar until crumbly. Set aside.

3. In a large bowl, whisk together 2 cups flour, granulated sugar, baking powder, and salt.

4. In a separate bowl, whisk the melted butter, eggs, milk, and vanilla extract until smooth.

5. Pour the wet ingredients into the dry ingredients and stir just until combined.

6. Fold in the cherries gently so they stay evenly distributed through the batter.

7. Divide the batter evenly between the muffin cups, filling each about three-quarters full.

8. Sprinkle the cobbler topping over each muffin.

9. Bake for 20 to 24 minutes, until the tops are golden and a toothpick inserted into the muffin portion comes out mostly clean.

10. Let the muffins cool in the pan for 5 minutes, then transfer them to a wire rack to finish cooling.