With oven rack placed in the middle position, preheat oven to 350F degrees. Process the tomatoes and onion in a food processor until smooth, about 15 seconds. Transfer mixture to a 4-cup liquid measuring cup and spoon off excess as needed, usually about 1/2 cup, until mixture measures 2 cups. (The excess tomato/onion mixture can be incorporated elsewhere in your menu like added to black beans before heating, etc. See notes for more ideas.)
Remove ribs and seeds from 2 jalapenos and discard; mince and set aside. Mince the remaining 1 jalapeno, leaving the ribs and seeds in it and set that one aside separate from the first 2 without the seeds/ribs.
Heat the 1/3 cup oil in a Dutch oven over medium-high heat for 1 to 2 minutes. Drop 3 or 4 grains of rice into the oil; if grains sizzle, oil is ready. Add rice and cook, stirring frequently, until light golden and translucent, 6 to 8 minutes. The oil will become quite "fizzy", which is normal.
Reduce heat to medium. Add garlic and the 2 seeded jalapenos and cook, stirring constantly, until fragrant, about 1 1/2 minutes. Stir in tomato-onion mixture, broth, tomato paste, and salt and bring to a boil. Cover, transfer pot to the oven and bake until liquid is absorbed and rice is tender, 30 to 35 minutes, stirring well after about 15 minutes.
Remove pot from oven and fold in cilantro and the last jalapeno, the one with the ribs and seeds (This will not be too spicy but if you want to add half the jalapeno, by all means). Serve with the lime wedges.