Puree 1 tablespoon sliced fresh basil and 1/2 teaspoon finely grated lemon zest in a mini chopper or food processor. Add 1/4 teaspoon sugar and 2 tablespoons lemon juice, and pulse until combined. With machine running, add 1/4 cup extra-virgin olive oil; season with coarse salt. Bring a pot of water to a boil. Add 1 1/2 tablespoons salt and 1 cup shelled fresh garden peas (from 1 pounds in pods). Reduce heat and vigorously simmer until tender and bright green, about 4 minutes; drain and transfer to a bowl. Add 1 tablespoon basil vinaigrette and partially crush with a potato masher. Season with salt and freshly ground pepper, then add 1 1/2 teaspoons thinly sliced fresh mint. Drizzle with more vinaigrette, garnish with basil sprigs and serve.