Place the potatoes into a large pot and cover with salted water. Bring to a boil over high heat, then reduce heat to medium-low, cover, and simmer until tender, about 20 minutes. Drain and allow to steam dry for a minute or two.
Preheat an oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking pan.
Transfer the potatoes to a food processor. Add 8 ounces Cheddar cheese, milk, sour cream, butter, dill weed, salt, and pepper. Process until smooth. Pour mixture into the prepared baking pan. Sprinkle with the remaining Cheddar cheese, then cover with aluminum foil
Bake in the preheated oven for 30 minutes. Remove foil and continue baking until the cheese is lightly browned, 15 to 20 minutes more.