Preheat the oven to 375°F (190°C).
Heat olive oil in a large oven-safe skillet or casserole dish over medium heat.
Add diced onion, carrots, and celery. Sauté for 5 minutes until vegetables are softened.
Add minced garlic and cook for 1 minute until fragrant.
Stir in the rinsed rice and cook for 2 minutes, stirring frequently.
Pour in the chicken broth and bring to a simmer.
Add the chicken pieces, dried thyme, dried parsley, paprika, salt, and black pepper. Stir to combine.
Cover the skillet or casserole dish with a tight-fitting lid or aluminum foil.
Bake in the preheated oven for 35 minutes, or until the rice is tender and the chicken is cooked through.
While the casserole is baking, whisk together nutritional yeast, coconut milk, cornstarch, and water in a small bowl until smooth.
After 35 minutes, remove the casserole from the oven and carefully stir in the coconut milk mixture.
Return the casserole to the oven, uncovered, and bake for an additional 5 to 10 minutes until the sauce thickens.
Remove from oven and let it rest for 5 minutes before serving.