1. Warm 1 Tbsp. oil in a skillet over medium-high heat. Sprinkle chicken with salt and pepper. Cook chicken, turning, for 10 minutes. Drain off fat. Pour in broth, cover, reduce heat to low; cook for 35 minutes. Remove chicken; let cool. Shred meat. Skim fat from cooking liquid; reserve liquid.
2. Put potatoes in a pot, cover with salted water; bring to a boil. Cook for 5 minutes; drain.
3. Warm remaining oil in a skillet over medium-high heat. Sauté potatoes, onion, bell pepper and white parts of scallions for 5 minutes. Add garlic, thyme, paprika, 1 tsp. salt and 1/2 tsp. pepper; sauté for 4 minutes. Add chicken; sauté for 3 minutes, adding reserved liquid as needed. Sprinkle with scallion greens before serving.