Heat a large skillet over high heat. Add the dry, unwashed rice, tossing or stirring constantly, until toasted and very brown and nutty, about 8 to 12 minutes. Transfer to a heatproof bowl.
Place a large Dutch oven or heavy-bottomed pot over medium heat. Add the schmaltz, garlic, carrots, onions and 5 teaspoons salt and cook, stirring occasionally, until the vegetables are tender and just beginning to brown, 6 to 8 minutes. Add the tomato paste and cook, stirring and scraping the bottom of the skillet, until fragrant and brick red colored, about 1 minute. Add the stock and bring to a boil. Stir in the rice, top with the peas and chile, reduce the heat to low, cover and cook undisturbed for 20 minutes. Check to see if all the liquid has been absorbed; if not, continue to cook and check again after 10 more minutes. Once the liquid has been absorbed, remove from the heat and let sit, covered, for 10 minutes before serving.