Prepare the pesto by combining all the ingredients, except the oil, in a food processor. Begin processing and with the motor running, slowly drizzle in the olive oil. Blend until smooth. Taste test and adjust seasonings if need be. Set aside.
Preheat the oven to 450°F. Toss the radishes with the oil and sprinkle with salt and pepper. Place on a parchment-covered baking sheet and roast in the oven until crisp-tender and lightly browned, 12-15 minutes. Toss halfway through cooking.
Cook pasta in a pot of boiling water until al dente. Drain pasta, reserving one cup of cooking liquid. Toss the pasta in a bowl with the pesto and roasted radishes. If need be, add the cooking liquid a little at a time if the pasta mixture is dry. Serve with grated parmesan cheese, salt, pepper and a few micro greens.