In a medium-size saucepan, heat olive oil over medium-high. Add onion. Remove from heat, and stir in vinegar, mustard, 3/4 teaspoon salt, and 1/4 teaspoon pepper.
In a large bowl, combine spinach, ham, and radishes. Drizzle onion mixture over salad, and toss to coat evenly. Garnish with hard-cooked eggs, and serve.