Rinse rice in a sieve under running water and drain.
Rinse asparagus, peel only the lower third, trim the ends and cut into bite-size pieces.
Rinse spinach and cook in little boiling salted water until wilted. Drain, rinse and drain. Rinse snow peas, trims ends, half crosswise and blanch in boiling salted water for about 4 minutes. Drain, rinse and drain.
Peel and press garlic. Heat 2 tablespoons oil in a pot and sauté garlic and asparagus. Remove and set aside.
Sauté the rice in 1 tablespoon hot oil. Gradually pour in broth and cook about 20 minutes, stirring occasionally, until the rice is al dente.
About 5 minutes before the end of cooking the rice, add asparagus snow peas and spinach and cook until heated through. Stir in butter in small pieces and the grated Parmesan cheese. Season with salt and pepper. Garnish with parsley and additional Parmesan cheese.