Heat 1 Tbsp vegetable oil in a large pot over medium - high heat. Crack eggs into pot, and scramble yolks. Salt and pepper to taste, and sprinkle with red pepper. Continue to scramble until eggs are cooked through - about 5 minutes.
Add garlic, onion, ginger, cabbage, and carrots along with additional 1 Tbsp vegetable oil and stir to coat in oil. Add soy sauce and cook for 15 minutes, stirring occasionally. Vegetables should be soft, and there should be some soy sauce left at the bottom of the pot. Add rice, and stir to toast in soy sauce.
Add vegetable stock, and water, as well as chili paste. Bring pot to a boil, then lower heat and let simmer covered for 20 minutes.
Stir to fluff rice, and serve or put away for lunch prep!