Prep the rice and vegetables. Rinse the rice in a fine-mesh strainer under cool water for 30 to 45 seconds, until the water runs mostly clear. Dice the onion into small, even cubes, finely dice the carrot, and mince the garlic.
Season the chicken. Pat the chicken pieces dry with a paper towel. In a small bowl, combine paprika, cumin, turmeric, thyme, salt, and black pepper. Sprinkle the seasoning over the chicken and toss until every piece is coated.
Brown the chicken. Heat olive oil in a large deep skillet over medium-high heat. Add the chicken in an even layer and cook for 4 to 5 minutes, turning once, until the edges are golden. The chicken does not need to be fully cooked yet.
Add the onion and garlic. Reduce the heat to medium and add the diced onion. Cook, stirring occasionally, for about 3 minutes until they begin to soften. Then add the garlic and cook for another minute until fragrant.
Stir in the carrot and rice. Add the finely diced carrot and stir to combine for 1 minute. Add the rinsed rice, stirring well to coat everything in the oil and spices.
Add the broth and bring to a simmer. Pour in the chicken broth and stir to combine. Increase the heat to medium-high and bring the mixture to a simmer, then reduce the heat to low. Cover the skillet with a lid.
Cook the mixture. Let everything simmer for 15 to 20 minutes on low heat, or until the rice is fully cooked and the chicken is tender and no longer pink in the center. Stir in the frozen peas during the last 2 minutes of cooking.
Season and finish. Fluff the rice gently with a fork and stir in the lemon juice. Adjust the seasoning with additional salt, if needed, before transferring to a serving dish.
Garnish and serve. Top with freshly chopped parsley and serve warm. Add optional lemon wedges for a bright finish.