Bring water to the boil in a saucepan. Add buckwheat; stir once. Reduce heat and simmer until buckwheat is tender yet firm to the bite, about 8 minutes.
Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to the boil. Add asparagus, cover and steam until tender, 2 to 6 minutes. Remove from steamer; cut into bite-size pieces.
Combine asparagus and pesto in a bowl; mix until coated. Add buckwheat; toss to combine. Top with Parmesan cheese.