Preheat oven to 425°F with rack in middle. Brush muffin cups with softened butter. Whisk together cornmeal, salt, baking powder, and baking soda in a large bowl. Whisk together corn, buttermilk, egg, and melted butter in another bowl, then stir into flour mixture until just combined. Stir in 1 1/2 cups cheese.
Divide batter among muffin cups and sprinkle with remaining 1/4 cup cheese. Bake until puffed and golden-brown and a wooden pick inserted into center of a muffin comes out clean, about 20 minutes. Turn out onto a rack to cool. Serve warm or at room temperature.
Make jalapeno butter while muffins bake: Stir together butter, jalapeno, and 1/4 teaspoon salt. Serve with muffins.