1. Place shallot in 2 cups ice water and let stand for 30 minutes. Drain and pat dry with paper towels.

2. Whisk vinegar, garlic, mayonnaise, 1/4 teaspoon salt, and 1/4 teaspoon pepper in nonreactive bowl until mixture appears milky and no lumps remain. Whisking constantly, slowly drizzle in oil. (Dressing should appear homogeneous, glossy, and slightly thickened, without pools of oil on surface.)

3. Gently toss avocados, 2 tablespoons dressing, and 1/2 teaspoon salt in bowl. Transfer avocados to large platter or individual plates.

4. Toss shallot, tomatoes, radishes, and basil with remaining dressing. Spoon tomato mixture over avocados and sprinkle with ricotta salata. Serve immediately.

Serves 6