In a blender, combine the roasted peppers, 1 tablespoon of the lemon juice, 1 teaspoon of the hot paprika, the sugar and ½ teaspoon salt. Puree, scraping the jar as needed, until smooth, about 30 seconds. Set aside.

In a large Dutch oven over medium-high, heat the oil until barely smoking. Stir in the onion, tomato and finely chopped banana pepper. Cover, reduce to medium and cook, stirring often, until the tomato has broken down and the onion is softened and light golden brown, about 10 minutes.

Stir in the sweet paprika, remaining 3 teaspoons hot paprika, broth and half of the pepper puree. Bring to a simmer, then cover, reduce to low and cook, stirring occasionally, for 30 minutes.

Stir in the sweet paprika, remaining 3 teaspoons hot paprika, broth and half of the pepper puree. Bring to a simmer, then cover, reduce to low and cook, stirring occasionally, for 30 minutes.

Add the chicken and stir until well coated. Bring to a boil over medium-high, then cover, reduce to medium-low and simmer, stirring occasionally, until a skewer inserted into the chicken meets no resistance, about 40 minutes.

Off heat, stir in the remaining 1 tablespoon lemon juice. Push the chicken to the side; add the remaining pepper puree and the sour cream to the liquid. Whisk to incorporate, then stir to combine the sauce and chicken. Taste and season with salt and black pepper. Serve garnished with the sliced banana pepper and with the dumplings and cucumber salad.