Cheddar Corn Muffins with Jalapeño Butter

For muffins:
5 tablespoons unsalted butter, melted and cooled, plus 1 tablespoon, softened, for brushing muffin cups
2 cups cornmeal (preferably stone-ground)
1 teaspoon salt
1 teaspoon baking powder
1/2 teaspoon baking soda
3/4 cup corn, thawed if frozen
1 1/4 cups well-shaken buttermilk (not powdered)
1 large egg
1 3/4 cups grated sharp Cheddar (5 1/4 ounces), divided

For jalapeño butter:
1 stick unsalted butter, softened
1 fresh jalapeño, finely chopped, including seeds


Equipment: a muffin pan with 12 (1/2-cup) muffin cups