Sunny-Side Beans

Ingredients:1 1/2 cups water12 ounces green beans, trimmed, cut in 1-inch pieces (about 3 cups)1 cup fresh shelled beans, fresh crowder peas or frozen baby lima beans1/4 cup minced onion2 tablespoons butter1/2 teaspoon salt4 large eggs, at room temperature (see tip)Freshly ground pepper to taste