Bring 2 quarts of salted water to a rapid boil.
While waiting for water to boil, add pesto ingredients to a food processor or high-speed blender; start with 1 tablespoon of water or olive oil and increase if needed. Blend until a thick but creamy pesto is achieved.
Once water is boiling, add spaghetti and return to a boil. Cook uncovered 9–11 minutes, stirring occasionally.
Drain pasta, and reserve some of the water. Return drained pasta to pot.
Combine drained spaghetti and pesto sauce in pot. Toss pasta to ensure even coating. Add some of the reserved pasta water if a thinner pesto sauce is desired.
To serve, divide pasta among four bowls and add extra peas, chopped basil and mint, and sliced radishes, if using. Enjoy!