For the dressing: In a jar, combine the olive oil, parmesan, salt, pepper, sugar, paprika, lemon juice, and garlic. Shake it up and store it in the fridge until using.
For the salad: In a large bowl, combine the greens, red onion, and radishes. Discard the garlic from the dressing and shake well again, then drizzle about half over the salad. Season with salt and pepper. Toss well, adding more dressing if needed.
Notes
Use the tops of your radishes as part of your total greens!