Preheat oven to 450°F with racks in upper and lower thirds.
Oil a four sided baking sheet with 2 tablespoons olive oil. Put cauliflower slices on oil, then turn to coat both sides. Sprinkle cauliflower with salt and pepper to taste. Roast cauliflower in top third of oven until tender and golden on edges, about 30 minutes.
Meanwhile, combine lemon, capers, 1/2 teaspoon salt, and 1/2 teaspoon black pepper, in a small bowl, then whisk in 1/4 cup olive oil.
Put chicken breasts between 2 sheets of plastic wrap and pound with flat side of a meat pounder until about 1/4-inch thick.
Oil another four sides baking sheet with remaining 2 tablespoons olive oil. Turn chicken paillards in oil and season with about 1/2 teaspoon salt and pepper total. When cauliflower is almost tender (after about 20 minutes), put chicken in bottom third of oven and bake until just cooked through, about 8 minutes, and cauliflower is golden on edges.
Arrange chicken over cauliflower, stir basil or parsley into vinaigrette and spoon over chicken.
Variations: Try the same vinaigrette with white wine vinegar and dill instead of lemon and basil or parsley.