Bring chicken broth to a simmer in a medium saucepan. Keep hot.

Pat pork dry with paper towel. Melt 2 tablespoons butter in a large heavy saucepan over medium heat. Add pork and cook until browned, 6 to 8 minutes. Remove from saucepan and set aside.

Add 2 tablespoons butter to saucepan and melt over medium heat; add leeks and garlic. Saute until wilted, about 5 minutes. Add rice; cook, stirring frequently, until rice is hot, about 3 minutes. Add hot broth, 3/4 cup at a time, stirring very frequently until rice is about half-cooked, allowing each addition to be absorbed before adding the next, about 15 minutes. Stir in asparagus, peas, and parsley. Continue adding broth and stirring until rice is tender but still firm to bite, about 8 to 10 minutes. Stir in pork and cheese; stir until cheese melts. Season with pepper.