In a large bowl, rinse rice in plenty of water, swishing the rice around with your fingers to wash off as much starch as possible. Drain well in a fine-mesh strainer, then spread on a paper-towel lined plate or clean kitchen towel to dry for at least 5 minutes.
In a 2- or 3-quart saucepan, heat 1 tablespoon oil over medium-high heat until shimmering. Add onion and cook until softened, 3 to 5 minutes. Add garlic and cook, stirring frequently until fragrant, about 30 seconds. Using a slotted spoon, transfer mixture to a blender, leaving as much oil in the pan as possible. Add ¼ cup (60ml) broth, tomatoes, and salt to the blender. Pulse to combine, then blend until completely smooth; set aside.
In the saucepan with the reserved oil, add the remaining 1 tablespoon oil and heat over medium-high heat until shimmering. Add rice and cook, stirring occasionally, until rice is golden and smells toasted, 5 to 8 minutes. Pour in the tomato mixture, stir to combine, and simmer until thickened, 3 to 5 minutes.
Add remaining 1 ¼ cups (290ml) broth and mix gently, taking care not to agitate the rice more than necessary. Stab the serrano chile once or twice with a fork to help release its flavor, then add it to the broth. Scatter the peas and carrots over the rice.
Cover and cook over medium heat until liquid is no longer visible on surface of rice, minimal steam is being generated, and rice has a noticeable “cooked” smell, 10 to 15 minutes. (You can open the lid a little at the 10-minute mark to check the rice’s progress, but try not to let too much steam out.)
Turn off heat and let rice sit, covered, for at least 10 or up to 20 minutes to absorb any remaining liquid. Fluff the rice with a fork and gently stir the peas and carrots throughout the rice, discard chile if desired, and serve.