Bring a medium pot of water to a boil. Cook ramen noodles, reserving seasoning packets, in boiling water until softened, about 3 minutes. Drain noodles and set aside.

Heat 1 tablespoon vegetable oil in a small skillet. Cook and stir beaten eggs in hot oil until scrambled and firm. Set aside.

Heat 1 teaspoon vegetable oil in a large skillet over medium heat. Cook and stir green onions in hot oil until softened, 2 to 3 minutes. Remove green onions to a plate; set aside.

Heat remaining 1 teaspoon vegetable oil in the same skillet over medium heat. Cook and stir carrots, peas, and bell pepper separately until softened, removing each to the plate with green onions when done.

Combine 2 tablespoons sesame oil with remaining 1 tablespoon vegetable oil in the same large skillet or a wok over medium heat. Fry cooked noodles in hot sesame-vegetable oil, tossing frequently, until golden, 3 to 5 minutes. Season with desired amounts of sesame oil, soy sauce, and reserved ramen seasoning packets; toss to coat. Stir in cooked vegetables, tossing frequently, until heated through, about 5 more minutes.