1. Peel and discard the tough outer layer of the fennel. Cut out the hard core. Use a serrated knife to slice the fennel crosswise as thinly as possible. Transfer to a large bowl. Whisk the oil and vinegar in a small bowl, and season with salt and pepper. Add 1 tbsp of the dressing to the fennel with the garlic, toss, and let stand for 1 hour.

2. Toss the mixed greens with the remaining dressing and season with salt and pepper. Divide the greens among 6 plates, then top with equal amounts of the fennel salad, and serve.