Beat eggs in a small bowl with a large pinch of salt and pepper to taste. Set aside.
Add the canola oil and 1 teaspoon sesame oil to a large non-stick skillet or wok and place over MEDIUM heat. Add the beaten egg to the hot skillet and cook, stirring, until it begins to form soft curds, about 30 seconds. Transfer the soft-cooked eggs to a plate and set aside.
Add the remaining 1 tablespoon sesame oil to the skillet (if skillet seems very dry, you can also add a little additional canola oil) and return it to MEDIUM heat. Add the carrots, and the white parts of the green onions, and cook, stirring frequently, until the carrots are fork tender, about 2 minutes. Add the garlic and ginger and cook, stirring, until fragrant, 1 minute.
Add the cooked rice, peas, ham and cooked eggs to the skillet. Pour in the soy sauce and cook, stirring until heated through, about 1 minute. Stir in the green parts of the green onions.
Serve immediately with Sriracha on the side.