Preheat your oven to 350°F (175°C) and grease your baking pan with a bit of butter or non-stick spray.
In a large mixing bowl, whisk together 3 cups of all-purpose flour, 1 tablespoon of baking powder, 1 teaspoon of salt, and ½ teaspoon of black pepper until well combined.
Stir in 4 oz of shredded sharp cheddar cheese and 3 oz of shredded Pepper Jack cheese into the flour mixture, ensuring they are evenly distributed.
In another bowl, combine 1 ¼ cups of milk, 3 tablespoons of melted unsalted butter, 1 lightly beaten large egg, and ½ cup of sour cream. Whisk these together until smooth.
Pour the wet mixture into the bowl with the dry ingredients. Stir gently until just combined—be careful not to overmix. The batter should be thick but not dry.
Transfer the batter into your prepared baking pan and smooth the top with a spatula. Bake in the preheated oven for 30-35 minutes or until the top is golden brown and a toothpick inserted into the center comes out clean.
Allow the bread to cool in the pan for about 10 minutes before transferring it to a wire rack to cool completely. Slice and enjoy your quick cheese bread warm or at room temperature!