In a medium skillet heat the oil over medium-high flame. Add diced potatoes, onion, and leeks. Saute until softened, about 3 minutes. Add minced garlic and continue to cook for another 2 to 3 minutes, until the garlic is soft, but not brown. Add the chicken stock and bring the liquid to a boil. Reduce the chicken stock until about 2 tablespoons of liquid remain in the pan. Crack the eggs over top, and cover with a lid. Reduce the heat to medium-low. Cook until the whites are set, about 15 minutes. Remove the pan from the heat, season with salt and pepper, and garnish with fresh basil.