Cook the pasta according to the package directions. Drain it and return it to the pot.
Meanwhile, heat the oil in a large saucepan over medium heat.
Add the leeks to the saucepan, season with the salt and ¼ 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 ¾ cup of the Pecorino. Simmer until the sauce has thickened slightly, about 4 minutes.
Add the sauce, lemon zest, and mint to the pasta pot and toss. Divide among shallow bowls and sprinkle with the remaining Pecorino and pepper.