Using the thinnest mandoline setting (1/8″ or less) slice the zucchini, squash, radishes and shallot into coins. Collect into a large mixing bowl and set aside.
Make the dressing by whisking together the garlic, lemon juice and vinegar. Slowly whisk in the olive oil to form an emulsion. Season with salt and pepper.
Toss the vegetable coins with the dressing and spread out over a serving platter or wide shallow bowl. Sprinkle lemon zest, grated horseradish, basil, mint and parmigiano reggiano cheese over the top of the salad.