Butter an 8 x 8" baking dish (20 cm x 20 cm).
Preheat oven to 375 F (190 C).
Use the grater attachment on the food processor (or another grater) to grate the cheddar cheese. Move to another container while you work with the wet ingredients. (I often put the grated cheese on a plate I'll be using for the meal.)
Add the cottage cheese, 1/2 of the milk, mustard, salt and pepper to the bowl of the food processor. Process until smooth. (or use a blender).
Add the uncooked pasta to the food processor bowl. (or add them to the blender jar).
Mix by hand until all of the pasta is coated.
Pour into prepared pan. Add the remaining milk all and but about 1/4 c. (~60 mL) of the cheese. Mix well. Cover with foil.
Bake for 30 minutes.
Stir, add chopped broccoli if using.
Bake for 20 minutes, covered.
Top with reserved cheese. Bake for 10 minutes, uncovered.
8" x 8" (20 cm x 20 cm) baking dish
Food processor with grater attachment (or blender and grater)
This recipe is designed for use with a food processor that has a grating tool. If you don't have that or don't want to use it, grate the cheese with another tool and use a blender to mix the milk, seasonings, and cottage cheese.
Adapted from a New York Times recipe by Julia Moskin