Heat oven to 375ºF. Coat the inside of a 9-by-5-inch loaf pan with nonstick spray and set aside.
Whisk together the all-purpose flour, wheat flour, baking powder, salt, sugar, and dill in a large mixing bowl. Add in the cheese and stir in the beer just to combine. Spread the batter evenly in the prepared pan. Sprinkle with the sunflower seeds, if using.
Bake on the middle rack of the oven until the bread reaches an internal temperature of 210ºF on a digital instant-read thermometer, 45 to 55 minutes.
Remove from the oven and cool in the pan for 10 minutes. Transfer the loaf to a wire rack to cool for 10 to 15 minutes before slicing and serving.