Preheat oven to 375°F. Grease a 9x5-inch loaf pan with 1 tablespoon of the melted butter.
In a large bowl, whisk together flour, baking powder, salt, and sugar. Stir in the cheddar and jalapeño until coated.
In a separate bowl, whisk together the beer, egg, and remaining 3 tablespoons melted butter.
Pour the wet ingredients into the dry ingredients and stir with a spatula until just combined—do not overmix; the batter will be thick and slightly lumpy.
Transfer the batter to the prepared loaf pan and smooth the top.
Bake for 45–50 minutes, until a toothpick inserted into the center comes out clean and the top is golden brown.
Let the bread cool in the pan for 10 minutes, then turn out onto a wire rack to cool slightly before slicing. Serve warm.