Pasta with English Peas and Morels

Name: Pasta with English Peas and Morels
Ingredients: 1/2 tsp. salt, plus more, to taste; 8 oz. (250 g) ditalini or other small tube pasta; 2 Tbs. olive oil; 4 oz. (125 g) morel mushrooms, halved lengthwise; 4 garlic cloves, chopped; Freshly ground pepper, to taste; 1/2 cup (4 fl. oz./125 ml) low-sodium vegetable or chicken broth; 1/2 cup (2 1/2 oz./75 g) shelled English peas (about 1/2 lb./250 g unshelled); 4 Tbs. grated Parmigiano-Reggiano cheese; Zest of 1 lemon; 2 Tbs. chopped fresh basil leaves