Preheat oven to 350 degrees F (175 degrees C). Grease a 9x5-inch loaf pan with vegetable oil.
Whisk flour, baking powder, salt, cayenne pepper, and black pepper together in a bowl. Stir cheese cubes into flour mixture until coated. Whisk milk, sour cream, melted butter, and egg in a separate bowl. Stir moist ingredients into flour and cheese mixture until just combined. Spread batter into prepared loaf pan.
Bake in the preheated oven until the top of the loaf is golden and a toothpick inserted into the center of the loaf comes out clean, 45 minutes to 1 hour. Let cool in pan 10 minutes before removing to finish cooling on a wire rack. Let cool 1 hour before serving.