In a Dutch oven, heat oil over medium-high heat. Season the chicken pieces with salt and pepper and dust with flour. Once oil is hot, fry the chicken pieces, turning occasionally, until browned on all sides, about 8 to 10 minutes. Remove chicken from pot and place on a plate, then tent with foil. Wipe Dutch oven clean.
Return Dutch oven to stove over medium heat. Melt bacon grease (or butter). Add onion, pepper, and garlic and cook until softened and starting to brown, about 8 to 10 minutes. Stir in crushed tomatoes and bring to a simmer. Reduce heat to low and let simmer for 15 to 20 minutes. Season with salt, white pepper, curry powder, parsley, and thyme and simmer for 5 more minutes. Return the chicken pieces to the Dutch oven and nestle down into sauce, spooning sauce over all of the pieces.
Using the lid as a guide, trace and cut out a circle of brown paper. Place the paper over top of the chicken and cover pot with the lid. Put pot into oven and cook for 45 minutes.
Remove pot from oven. Carefully remove the chicken pieces from the pot and place them in the center of a large platter. Stir the almonds and dried currants into the sauce. Spoon the rice around the rim of the platter surrounding the chicken. Pour the sauce over the chicken and rice. Garnish with parsley and serve.