Grate tomatoes into a bowl using a box grater; discard tomato skins.
Heat vegetable oil in a heavy skillet over medium-high heat and cook onion until translucent, stirring often, about 5 minutes. Stir garlic into onion and cook until fragrant, about 1 minute.
Stir rice into onion mixture and cook, stirring often, until rice is lightly toasted, about 3 more minutes. Stir grated tomato, chicken broth, and tomato sauce into the rice. Bring mixture to a boil.
Mix in jalapeno pepper, cilantro, and salt; reduce heat to low. Cover skillet and simmer until rice has absorbed the liquid, about 15 minutes. Do not lift the cover while the rice is cooking.
Turn off heat and let rice stand covered for 8 minutes. Fluff with a fork before transferring rice to a serving dish.