Set a large skillet over medium-high heat and add the olive oil. Pat the chicken thighs dry and dredge them in flour, shaking off the excess. Brown the chicken in batches until deeply golden on both sides. This step adds flavor and a nice crust. Remove the chicken to a plate and set aside.
In the same skillet, lower the heat a touch and add the sausage pieces. Cook until they start to brown and render some fat. They don’t need to be fully cooked through, just well colored on the outside.
Add the onion slices to the pan and sauté until they become translucent and a bit caramelized around the edges. Stir in the garlic and cook for about 30 seconds until fragrant.
Pour in the white wine to deglaze the pan, scraping up any browned bits from the bottom. Let it reduce by about half, which concentrates the flavors.
Return the chicken to the skillet. Add the chicken broth, lemon zest, lemon juice, and sliced peppers. Bring to a gentle simmer, then reduce the heat so the chicken cooks through and the sauce thickens slightly.
Stir in the capers and a few knobs of butter. Let the butter melt into the sauce, creating a glossy finish. Taste and adjust with salt and pepper as needed.
Simmer for about 15 minutes, or until the chicken reaches an internal temperature of 165 F and the flavors meld. If the sauce seems thin, you can simmer a bit longer or whisk in a touch more butter.
Finish with a quick sprinkle of chopped parsley, if using, and serve hot. The dish goes beautifully with crusty bread, mashed potatoes, or a simple green salad.