Pat chicken dry. Season with salt, pepper, garlic powder, and paprika.
Heat oil in Dutch oven over medium-high heat.
Add chicken skin side down. Cook 5 to 6 minutes per side until golden.
Remove chicken. Set aside.
Reduce to medium. Add butter.
Add onion. Cook 5 to 6 minutes until soft and golden.
Add garlic. Cook 30 seconds.
Sprinkle flour over onions. Stir 1 minute.
Slowly pour in broth while stirring constantly.
Add water, thyme, and bay leaf. Stir.
Bring to simmer until gravy thickens.
Stir in rice. Distribute evenly.
Nestle chicken into rice skin side up.
Bring to gentle boil.
Reduce to low. Cover with tight lid.
Cook 30 to 35 minutes without lifting lid.
Check rice at 30 minutes. Cook 5 more minutes if needed.
Remove from heat. Let sit covered 5 minutes.
Remove bay leaf. Adjust seasoning.
Garnish with parsley and green onions.
Serve hot with chicken on top of rice.