Crumble the chorizo into a large pot and cook over medium heat until browned, about 5 minutes, turning and breaking it up for even browning. Use a slotted spoon to remove the chorizo while 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 occasionally until translucent at the edges. Add the minced garlic and cook for 1 minute, stirring until fragrant and light golden.

Stir in the long-grain white rice and toast for 2-3 minutes over medium heat, stirring frequently, until the grains look slightly drier and lightly opaque with a toasty aroma.

Add the chicken broth, diced tomatoes with their juice, cumin, chili powder, and salt to the pot. Bring to a simmer, cover, and cook for 15 minutes, until the liquid is absorbed and the rice is tender with no pooling.

Fluff the rice with a fork to separate the grains, then stir in the cooked chorizo, chopped cilantro, and the lime juice for bright color throughout. Let the pot rest uncovered for 5 minutes so the final steam settles, then serve.