Preheat your broiler on high, then add the tomatoes and garlic to a heavy-duty broiler pan. Broil until the tomato tops are blackened, then flip and broil the other side until blackened. Squeeze the garlic out of its skins, then add to a blender jar along with the tomatoes and onions. Blend until it's as smooth as possible.
While the tomatoes are broiling, rinse the rice in a rice strainer until the water runs clear. Let drain thoroughly, shaking and stirring until no more water drips through the strainer.
Heat the oil over medium-high heat in a heavy-bottomed stockpot. Once the oil is shimmering, fry the rice until just turning color, stirring, and turning over constantly so it will cook evenly and doesn't stick. About 8-10 minutes.
Add tomato puree to the fried rice. Over medium-high heat, cook, stirring constantly until most of the moisture has evaporated out of the puree. About 3-4 minutes.
Reduce the heat to medium-low, add the chicken stock, carrot, peas, parsley serrano peppers, and salt—cover and cook for ten minutes. Remove from heat and let sit for an additional 20 minutes. Fluff with a fork, and serve.