Remove the tips and the first two joints of the wing bone, leaving the bone attached to the breast. Pound the breast 1/2-inch thick between two pieces of plastic wrap, being careful not to separate the meat from the bone, pat it dry, and season with salt and pepper. Dredge the chicken breasts in the flour, shaking off the excess, dip them in the egg, letting the excess drip off, and coat them with the bread crumbs. In a large heavy skillet cook the garlic in oil and the butter over moderately high heat, stirring until its golden and discard it. Saute the chicken breasts in the fat, turning them once, for 4 minutes, or until they are golden brown, and transfer them to paper towels to drain.
Make the salad: In a small bowl whisk together the vinegar, mustard, thyme, salt and pepper to taste, add the oil in a slow, even stream, whisking until all the dressing is emulsified. In a bowl toss the arugula, tomatoes and carrots with some dressing.
Arrange each chicken breast on a plate, divide the salad between the plates, and garnish each with a lemon wedge.
Recipe courtesy of Gourmet Magazine