Brown the chicken: Season the chicken generously with salt and pepper. Heat oil in a Dutch oven over medium-high. Add chicken, skin side down, and sear until golden brown and crisp, 5–7 minutes per side. Transfer to a plate. Pour off all but 1 tablespoon fat.
Build the base: Melt butter (2 tablespoons) in the pot. Add onions (2) and cook, stirring often, until soft and golden, 6–8 minutes. Add garlic (6) and cook another 1–2 minutes until fragrant. Stir in paprika (4 tablespoons), flour (1 tablespoon), and cayenne; cook 2–3 minutes until the paprika blooms and flour loses its raw taste.
Deglaze with wine: Pour in white wine (1/2 cup) and simmer, scraping up browned bits, until mostly reduced, 2–3 minutes.
Dissolve Better Than Bouillon: In a small bowl, whisk Better Than Bouillon (2 teaspoons) with boiling water (1/4 cup) until completely dissolved.
Add tomatoes + broth: Stir in crushed tomatoes (1 cup), broth (1 cup), dissolved Better Than Bouillon, 1 1/2 teaspoons salt, and 1/2 teaspoon black pepper. Simmer until smooth and slightly thickened, 3–4 minutes.
Braise the chicken: Nestle chicken into the sauce, skin side up (mostly submerged). Cover and simmer gently on the stovetop for 45–50 minutes, until chicken is tender but skin remains intact.
Thicken the sauce: Transfer chicken to a platter. The sauce should be thick enough to coat the back of a spoon. If it doesn't, increase heat and simmer sauce uncovered until its achieved the spoon-coating consistency.
Finish with dairy: Remove pot from heat. Stir in sour cream (1 cup) and heavy cream (2 tablespoons). Return chicken to the sauce, turn it over to coat, and heat briefly to warm through.
Serve: Place chicken over buttered egg noodles. Spoon sauce generously over top, sprinkle with fresh dill or parsley, and serve immediately.