In a large skillet over medium heat, heat 1 Tbsp. vegetable oil. Add eggs and let sit for a few seconds before lightly scrambling and folding eggs over themselves, 45 seconds to 1 minute. Transfer to a plate.
In same skillet over medium heat, heat remaining 1 Tbsp. vegetable oil. Cook onion and carrot, stirring occasionally, until vegetables are tender, about 7 minutes. Add pork; season with salt and pepper. Cook, breaking up with a spoon, until starting to caramelize, about 3 minutes. Stir in garlic, peas, and ginger and cook, stirring frequently, until fragrant, about 1 minute.
Add rice, then stir in scallions, soy sauce, hoisin sauce, and sesame oil. Fold in scrambled eggs.