Preheat oven to 350°F and position rack in the middle.
Blend tomatoes and onion in a food processor until smooth. Adjust to 2 cups.
Seed and mince two jalapeños; mince the third with seeds and set aside separately.
Rinse rice under cold water until water runs clear, about 1½ minutes. Shake dry.
Heat oil in an oven-safe sauté pan or Dutch oven over medium-high.
Add rice and cook, stirring, until golden and translucent, 6 to 8 minutes.
Reduce heat. Add garlic and seeded jalapeños. Cook until fragrant, about 1½ minutes.
Stir in tomato-onion puree, broth, tomato paste, and salt. Bring to a boil.
Cover and transfer to the oven. Bake for 30 to 35 minutes, stirring after 15 minutes.
Stir in cilantro and minced jalapeño with seeds, to taste.
Serve with lime wedges.