Crumble the chorizo into a large pot and cook over medium heat until browned, about 5 minutes, stirring occasionally so it renders evenly; visual cue: the fat becomes golden and the bits look crisp at the edges. Remove the browned chorizo with a slotted spoon, leaving the drippings in the pot.

Add the olive oil to the pot and sauté the diced onion over medium heat until softened, about 3 minutes, stirring to coat; visual cue: onion turns translucent and fragrant. Add the minced garlic and cook for 1 minute, stirring constantly so it doesn’t brown.

Stir in the long-grain white rice and toast for 2-3 minutes over medium heat, stirring frequently; visual cue: grains look slightly opaque and smell nutty.

Add the chicken broth, diced tomatoes with their juice, cumin, chili powder, and salt. Bring to a simmer, cover with a lid, and cook for 15 minutes, keeping the surface at a steady simmer; visual cue: liquid is mostly absorbed and rice grains are tender.

Fluff the rice with a fork, then stir in the cooked chorizo, chopped cilantro, and lime juice; visual cue: the rice looks evenly speckled and glossy from the lime and drippings. Let the pot rest, covered, for 5 minutes before serving.