Bring 1 1/2 quarts water to boil in a medium pot. Add potatoes and 1 tsp. salt. Lower heat and simmer until potatoes are tender but not falling apart, 8 minutes. Drain and set aside.
Warm oil over medium heat in a large nonstick skillet with an ovenproof handle. Add onion and cook until softened, 3 minutes. Add bell pepper and cook until softened, stirring occasionally, 2 minutes. Add potatoes and 1/2 tsp. salt and cook, stirring, until they just start to brown, 6 to 8 minutes.
Preheat broiler. Whisk together eggs, ham and parsley; season mixture with pepper. Distribute vegetables evenly in pan and pour in egg mixture. Cook over medium-low heat, occasionally sliding a thin spatula around edges of pan to loosen eggs as they set. Continue to cook until frittata is set except for top, 7 minutes.
Place pan under broiler and cook until top is golden, 1 to 2 minutes. Cut into wedges and serve.