Season the chicken on both sides with the salt and black pepper.
Heat the olive oil in a large, deep skillet over medium heat. When the oil is hot but not smoking, add the chicken skin-side down. Cook for 3–4 minutes, until the skin is lightly browned. Flip and cook 2–3 minutes more to brown the other side.
Remove the skillet from the heat and transfer the chicken to a plate. Do not worry if it is not cooked through; it will finish cooking in the sauce.
Return the skillet to medium heat. Do not wash or wipe. Add the butter, and once melted, add the onion. Cook for 1–2 minutes, stirring frequently, until the onions begin to soften.
Stir in the garlic and Italian seasoning. Cook for about 30 seconds, stirring often, until fragrant.
Slowly pour in the white wine, scraping up any browned bits from the bottom of the skillet. Cook for 1–1½ minutes, allowing the wine to reduce slightly.
Add the chicken broth and cannellini beans and stir well.
Nestle the chicken back into the skillet, skin-side up. Bring to a gentle simmer, then reduce the heat to medium-low. Cover and cook for 10–15 minutes, checking after 10 minutes, until the chicken is cooked through or very close to reaching 165°F internally.
Scatter the greens evenly over the skillet. Cover and cook for 1–2 minutes, until just wilted. Gently stir them into the beans and broth and cook 1–2 minutes more.
Check that the chicken has reached an internal temperature of 165°F at the thickest part.
To Serve: If serving over rice or pasta, spoon it into a shallow bowl. Ladle the beans and broth over the base, then top with a piece of chicken and some of the wilted greens. Serve with a side of sliced cherry or grape tomatoes for a pop of color and a touch of acidity.