How to Make It
In a large skillet, heat the butter and 1 tablespoon of the olive oil over medium-high heat. Season the chicken with salt and black pepper. Add the chicken to the skillet, making sure to not overcrowd the pan. Cook until richly golden brown and seared, about 4 minutes per side. Add the white wine to the chicken and deglaze the pan. Transfer the chicken and the juices to the slow cooker.
Return the skillet to the stove and set over medium heat. Pour in a 1/2 tablespoon of olive oil and add the onions, garlic, paprika, and red pepper flakes to the pan. Cook until the onions have lightly browned, about 4 minutes. Add the spiced onion mixture to the slow cooker. Pour in the chicken broth and crushed tomatoes and stir to combine. Cover and cook for 3 hours on high, until the chicken is tender.
Transfer the chicken to a work surface and, using two forks shred the meat and discard the bones. Stir the shredded chicken into the sauce, add the caper berries, and season with salt and black pepper to taste.
To serve, bring a pot of salted water to a boil, cook the pasta until al dente and drain, reserving 1/2 cup of pasta water. Transfer the pasta to one large skillet set over medium heat and add the chicken cacciatore and pasta water to the noodles; toss until the linguine is thoroughly coated. Transfer to serving bowls, sprinkle with freshly grated Parmesan cheese, drizzle with olive oil, and garnish with chopped parsley.