Once hot, grill bread 2-3 minutes per side or until slightly charred. Remove from grill and roughly chop into cubes once slightly cooled.
Combine the tomatoes, green beans, and squash in a medium bowl and toss with 1 tablespoon olive oil and ¼ teaspoon salt and pepper. Transfer veggies to a grill pan and grill 10-12 minutes, stirring occasionally.
While veggies grill, whisk together the remaining 2 tablespoons olive oil, vinegar, and remaining ¼ teaspoon salt in a large bowl. Add the radicchio, grilled vegetables, and bread cubes; toss well.
Divided salad into 3 bowls and top with cheese and eggs. Serve immediately.