Season the chicken. Pat the chicken dry and season with salt, pepper, and half the smoked paprika. This builds flavor from the start.
Brown the chicken. Heat 1–2 tablespoons of olive oil in a large pot or Dutch oven over medium-high. Sear the chicken in batches until lightly browned, about 3–4 minutes per side.
Don’t cook it through yet. Transfer to a plate.
Sauté the aromatics. Lower heat to medium. Add a splash of oil if needed, then cook the onion, celery, and carrots with a pinch of salt for 5–6 minutes, stirring often, until softened and fragrant.
Add garlic and tomato paste. Stir in the garlic, remaining smoked paprika, thyme, and rosemary.
Cook 1 minute. Add tomato paste and cook another 1–2 minutes until it darkens slightly. This step adds depth.
Build the base. Sprinkle flour over the veggies and stir for 30 seconds.
Slowly add the chicken broth while stirring to avoid lumps. Add bay leaves and potatoes, then return the chicken and any juices to the pot.
Simmer gently. Bring to a simmer, then reduce heat to low. Cover and cook for 20–25 minutes, stirring occasionally, until the potatoes are tender and the chicken is cooked through.
Add green veggies. Stir in green beans and cook 5 minutes.
Add peas and kale or spinach and cook 2–3 minutes more, until greens are wilted and bright.
Finish with freshness. Remove bay leaves. Add lemon zest and a squeeze of lemon juice. Stir in parsley.
Taste and adjust salt and pepper. If you want it thicker, simmer uncovered a few more minutes.
Serve warm. Ladle into bowls and drizzle a tiny bit of olive oil on top, if you like. Crusty bread on the side is always a good move.