Grate tomatoes into a bowl using a box grater; discard tomato skins.

Heat vegetable oil in a heavy skillet over medium-high heat. Add onion; cook and stir until tender, about 5 minutes. Stir in garlic and cook until fragrant, about 1 minute.

Stir in rice and cook, stirring often, until rice is lightly toasted, about 3 more minutes. Stir in grated tomato, chicken broth, and tomato sauce; bring mixture to a boil.

Stir in jalapeño pepper, cilantro, and salt; reduce heat to low. Cover the skillet and simmer until liquid has been absorbed, about 15 minutes. Do not lift the cover while rice is cooking.

Turn off the heat; let rice stand, covered, for 8 minutes. Fluff with a fork before transferring rice to a serving dish.