How to Make It
Cook pasta in a large pot of generously salted water according to package directions. Drain, reserving 1 cup pasta water. Set aside.
Melt butter in a large skillet over medium. Add leeks and cook, stirring often, until very soft, about 4 minutes. Add half-and-half and cheese; cook, stirring constantly, until melted and thickened, 3 to 4 minutes. Stir in peas, salt, and ¼ teaspoon pepper. Cook, stirring often, until peas are bright green and tender, about 1 minute.
Add pasta and ½ cup pasta water to skillet, stirring gently, until sauce thickens, about 1 minute. Add remaining ½ cup pasta water, if needed, to loosen sauce. Top with chives, lemon zest, and remaining ¼ teaspoon pepper.