Preheat oven to 350 degrees. Heat oil in a 10-inch nonstick ovenproof skillet over medium-high heat. Add green beans, ham, and scallions (skillet will be full). Cover and cook, stirring occasionally until green beans are crisp-tender, about 6 minutes.
In a large bowl, whisk together eggs, cheese, 1 teaspoon salt, and 1/4 teaspoon pepper; add to skillet, and tilt to distribute evenly. Gently press down on vegetables to cover them with egg mixture. Cook, without stirring, until edges are slightly set, about 1 minute.
Transfer to oven; bake until center is set, 25 to 30 minutes. Run a wooden or rubber spatula around edges; slide frittata onto a platter, and cut into 4 wedges.