Place rice in a fine mesh strainer and rinse under cold water until water runs mostly clear, about 1 minute. Shake well to drain - this removes excess starch so the grains stay separate.

Heat oil in a large skillet over medium-high heat until shimmering. Add rinsed rice and cook, stirring frequently, until grains are lightly golden and smell nutty, 4 to 5 minutes. Do not let them brown deeply.

Push rice to edges of pan, add onion to center, and cook until softened and translucent, about 3 minutes. Stir in garlic and cook 30 seconds until fragrant.

Add tomato sauce, diced tomatoes with their juices, broth, salt, cumin, chili powder, and oregano. Stir well to combine, scraping any toasted bits from the bottom of the pan.

Bring to a full boil, then immediately reduce heat to low, cover tightly, and simmer for 18 to 20 minutes. Do not lift the lid. Rice is done when liquid is absorbed and small steam holes appear on the surface.

Remove from heat and let stand, covered, for 5 minutes. Uncover, fluff gently with a fork, and fold in cilantro if using. Serve with lime wedges.