Preheat oven to 400 degrees F. Season chicken thighs on both sides with Italian seasoning, paprika, 1.5 tsp. salt, and 0.25 tsp. pepper. Heat olive oil in a large oven-safe skillet over medium-high heat. Add chicken skin-side down and cook until deep golden brown, about 4 minutes per side. Transfer to a plate.

Return skillet to medium-high heat and add the reserved sun-dried tomato oil. Add garlic and cook, stirring, until fragrant, about 1 minute. Add wine and stir, scraping up any brown bits from the pan, until reduced by half, about 1 minute. Add chicken broth then slowly stir in heavy cream. Bring to a gentle simmer and stir in gnocchi, sun-dried tomatoes, and 0.5 tsp. salt. Nestle chicken back into the pan skin-side up.

Transfer skillet to the oven and bake until chicken is cooked through and an instant-read thermometer inserted into the thickest part registers 175 degrees F, 14 to 16 minutes.

Carefully remove skillet from oven. Transfer chicken to a plate. Add baby spinach and Parmesan to skillet. Cook over medium heat, stirring, until spinach wilts, about 2 minutes. Return chicken to skillet. Taste and adjust salt and pepper before serving.