Heat olive oil and butter together in a large pot over medium-high heat until melted and shimmering.
Add chopped onion and minced garlic, cooking while stirring occasionally until onions become translucent, about 5 minutes.
Mix in the carrot and celery pieces, cook for an additional minute to soften slightly.
Sprinkle in the Vegeta stock powder, dried parsley, thyme if using, and black pepper. Pour in the chicken broth and water, stirring to combine.
Place the bone-in chicken thighs into the pot, cover with a lid, and reduce heat to maintain a gentle simmer for 30 minutes, occasionally skimming off any foam that appears.
Lift the lid and stir in the uncooked rice, cover again and let it simmer for another 15 minutes until the rice is tender.
Remove the pot from heat, take the chicken out and shred it with two forks, discarding the bones.
Fold the shredded chicken back into the soup along with half of the fresh parsley, then season with salt to taste.
Serve the soup in bowls and sprinkle the remaining parsley on top for garnish.