Heat 2 tablespoons of olive oil in a large skillet over medium-high heat.
Add the chicken pieces and sauté until golden and cooked through, about 5–7 minutes; remove any excess juices if necessary.
Add the finely chopped onion to the skillet and sauté with the chicken for about 3 minutes, until softened.
Add the grated carrot and sauté for 2 more minutes until it softens.
Stir in 2 tablespoons of butter and 1/4 cup ketchup until the butter melts and everything is evenly coated.
Add the rinsed rice to the skillet and sprinkle with 1 teaspoon salt, 1/8 teaspoon black pepper, and 1/8 teaspoon Cayenne pepper; stir to combine.
Transfer the mixture to a rice cooker and add 2 1/2 cups water or low-sodium chicken broth; cook on the White Rice setting until done.
Or, to cook on the stovetop: place the mixture in a heavy pot with a tight-fitting lid, add 2 1/2 cups water, bring to a gentle simmer, then reduce heat to low and cook for about 20 minutes, until the liquid is absorbed and rice is tender.
Let the plov rest covered for 5 minutes, then fluff with a fork and serve.