Melt the butter in a saucepan over medium heat. Stir in the quinoa, and cook 2 minutes until toasted. Pour in the chicken broth, onion, garlic, thyme, and black pepper. Cover, and let come to a boil. Once boiling, stir in the frozen peas and asparagus pieces. (Wait a little longer to add asparagus if you prefer it more firm.)Recover, reduce heat to medium-low, and continue simmering until the quinoa is tender and has absorbed the chicken stock, 15 to 20 minutes.
Stir in half of the Pecorino Romano cheese and the parsley until evenly mixed. Scoop the quinoa into a serving dish, and sprinkle with the remaining Pecorino Romano cheese to serve.