Cook the pasta according to the package directions.
Meanwhile, heat the oil in a large saucepan over medium heat. Add the leeks, season with the salt and 1/4 teaspoon of the pepper, and cook, stirring occasionally, until soft, about 7 minutes. Add the garlic and peas and cook for 2 minutes more. Stir in the cream and 3/4 cup of the Pecorino. Simmer until the sauce has thickened slightly, about 4 minutes.
Drain the pasta and return it to pot. Add the sauce, lemon zest, and mint and toss. Divide the pasta among shallow bowls and sprinkle with the remaining Pecorino and pepper.
Tip: Sugary and slightly crunchy, fresh peas are well worth the extra effort of shelling during the brief period in the spring when they're available. You can use 2 pounds of fresh peas (2 cups shelled) in place of the frozen ones called for in this recipe.