Combine 1 cup of the flour, 1 tablespoon of the marjoram, 1 teaspoon of the paprika and some salt and black pepper in a low-sided dish. Stir until blended.
Heat a large Dutch oven over medium-high heat; add the butter and oil. Heat until the butter has melted and the oil is shiny.
Sprinkle the chicken all over with salt and black pepper. Next, dredge the chicken in the seasoned flour on all sides. Shake to remove excess flour before placing the chicken into the hot pot. Working in batches if necessary, sear the chicken on both sides until golden brown, about 4 minutes per side. Remove the chicken to a plate and set aside.
Add the onions to the pot and reduce the heat to medium. Sprinkle with the sugar and some salt and black pepper. Cook, stirring occasionally, until the onions have softened and turned golden, about 12 minutes. Add the garlic and bell peppers and cook for 1 minute more. Add the tomato paste, chicken broth, red pepper flakes and the remaining 1 tablespoon marjoram and 2 teaspoons sweet paprika; stir to combine.
Place the chicken back in the pot, nestling it in the sauce. Reduce the heat to low and simmer, covered, until the chicken is very tender and reaches an internal temperature of 165 degrees F, about 50 minutes.
Remove the chicken to a serving dish. Mix the sour cream with the remaining 2 tablespoons flour in a medium bowl. Stir the mixture into the sauce.
Pour the sauce over the chicken and sprinkle generously with dill.