In a 4- to 5-quart pan, bring 2 to 3 quarts of water to boiling over high heat.
Meanwhile, pull off and discard stem ends and strings from peas. Rinse and drain.
When water boils, add pasta, pushing down into water. Cook until almost tender to bite, about 3 minutes. Add peas and cook until they turn bright green, about 2 minutes.
Drain peas and pasta well in a colander.
In the pan, combine garlic and butter over high heat, stirring until butter melts. Add peas and pasta and mix until pasta stops sizzling, about 1 minute.
Add about 2 teaspoons of the lemon peel, 2 tablespoons of the lemon juice, and about 1 tablespoon mint to pan. Mix.
Put pasta mixture in wide soup bowls, swirling to make a well in the center. Spoon crème fraîche into the center of bowls and sprinkle with remaining peel, mint, and lemon juice. Add salt and pepper to taste.