Bring a large pot of lightly salted water to a boil. Add penne and cook, stirring occasionally, until tender yet firm to the bite, about 11 minutes.

Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add asparagus, cover, and steam until tender, 3 to 6 minutes. Remove asparagus and cut into 2-inch pieces.

Preheat the oven to 350 degrees F (175 degrees C). Grease a casserole dish.

Combine penne pasta and asparagus in the greased casserole dish. Mix milk, Parmesan cheese, eggs, dill, salt, and pepper in a bowl; pour over asparagus mixture.

Bake in the preheated oven until topping is set and lightly browned, about 20 minutes.