Rinse the rice in a fine-mesh strainer under cold water until the water runs clear; drain very well.
Heat the oil in a large saucepan or deep skillet with a tight-fitting lid over medium-high heat. Add the rice and cook, stirring constantly, 3-4 minutes until the grains turn golden and smell nutty.
Push the rice to one side. Add the onion and cook 2-3 minutes until softened; stir in the garlic and cook 30 seconds more. Stir everything together.
Stir in the tomato sauce, chicken broth, cumin, tomato bouillon, and pepper. Bring to a boil.
Cover tightly, reduce the heat to the lowest setting, and simmer 18-20 minutes WITHOUT lifting the lid, until the liquid is absorbed.
Remove from the heat and let stand, still covered, for 10 minutes.
Uncover, fluff with a fork, and fold in peas and carrots if using. Garnish with cilantro and serve with lime wedges.