Pat the chicken thighs very dry with paper towels. Season both sides generously with salt and pepper.
Heat the olive oil and butter in a large, oven-safe skillet over medium-high heat.
Place the chicken thighs skin-side down in the hot skillet. Sear for 8 to 10 minutes without moving them until the skin is deep golden brown and crisp.
Flip the chicken thighs and cook for 2 minutes on the flesh side. Remove the chicken from the skillet and set aside on a plate. Drain off all but 1 tablespoon of the rendered fat.
Reduce the heat to medium. Add the chopped onion to the skillet and cook until softened, about 3 minutes.
Add the minced garlic and cook for 1 minute until fragrant. Do not let the garlic burn.
Pour in the white wine or broth to deglaze the pan, scraping up any browned bits from the bottom. Let this reduce by half, about 2 minutes.
Stir in the heavy cream, chicken broth, Italian seasoning, salt, and pepper. Bring the sauce to a gentle simmer.
Return the chicken thighs to the skillet, nestling them into the sauce, skin-side up (keep the skin above the liquid if possible).
Simmer gently for 10 to 15 minutes, or until the internal temperature of the chicken reaches 165 degrees Fahrenheit. The sauce will thicken slightly.
Stir the Parmesan cheese into the sauce until melted and smooth. Taste and adjust seasoning if needed.
Garnish with fresh parsley before serving the chicken thighs over the creamy garlic sauce.
Notes
For the crispiest skin, ensure the chicken is completely dry before searing.
If your sauce becomes too thick while simmering, add a splash more broth or cream to reach your desired consistency.
Serve this dish with mashed potatoes or egg noodles to soak up the extra sauce.