Season the chicken. Cut the chicken thighs into fairly large bite-size pieces. Add the salt, black pepper, and paprika, then toss until the chicken is evenly coated.
Brown the chicken. Heat the olive oil in a large deep skillet or Dutch oven over medium-high heat. Brown the chicken in batches until nicely golden on the outside. It does not need to cook through yet. Transfer to a plate and set aside.
Soften the vegetables. Add the onion, carrots, and celery to the same pan. Cook over medium heat for about 5 minutes, stirring occasionally, until the vegetables begin to soften.
Add butter and garlic. Stir in the butter and minced garlic. Cook briefly, just until the butter melts and the garlic becomes fragrant.
Build the stew base. Sprinkle the flour over the vegetables and stir until evenly coated. Cook briefly, then add the salt, dried thyme, and black pepper. Stir well.
Add the broth. Slowly pour in the chicken broth while stirring, scraping up the flavorful browned bits from the bottom of the pan.
Add potatoes and chicken. Add the potatoes and return the browned chicken along with any juices from the plate. Bring everything to a gentle simmer.
Give the potatoes a head start. Cover the pan and simmer gently for about 15 minutes. This gives the potatoes time to begin softening before the tomato paste goes in.
Add the tomato paste. Scoop about 1/2 cup of hot broth from the pan into a small bowl and stir in the tomato paste until smooth. Pour the mixture back into the stew, then add the Worcestershire sauce and bay leaves. Stir gently to combine.
Finish simmering. Cover again and continue to simmer gently for another 10 to 15 minutes, until the potatoes and carrots are tender and the sauce has thickened nicely.
Add the peas. Stir in the frozen peas during the last 3 to 5 minutes of cooking, just until warmed through.
Finish the stew. Remove the bay leaves, taste, and adjust the seasoning if needed. Stir in the fresh parsley.
Serve. Spoon the chicken stew into bowls while warm, making sure each serving gets plenty of tender chicken, potatoes, vegetables, and rich savory sauce. Finish with a little extra parsley if you like.