Preheat oven to 400°. Coat 6 cups of a standard nonstick muffin tin with cooking spray.
Tuck 1 ham slice into each muffin tin cup, trying to make as much of a cup shape as possible, with the edges sticking out the top.
Stir together mozzarella, tomatoes, pesto, and breadcrumbs in a bowl. Season with ¼ teaspoon each of the salt and pepper.
Divide mixture among the ham cups. Carefully crack an egg into each cup. Bake in until the tomato juices are lightly bubbling and egg whites are set (~ 15 minutes)
Toss together salad greens, oil, vinegar, and remaining ¼ teaspoon each salt and pepper in a large bowl to make a simple salad.
Let ham cups cool slightly (~1 - 2 minutes). Unmold them by slipping a knife under the cups and gently transferring them to a plate.
Serve alongside dressed greens.