Heat olive oil in a large skillet over medium-high heat. Season chicken pieces with salt, pepper, and paprika, then brown for 4-5 minutes per side until golden. Remove chicken to a plate and set aside.
In the same skillet, add butter and diced onion. Sauté for 2-3 minutes until the onion softens, then add minced garlic and cook 30 more seconds until fragrant and golden.
Add sliced mushrooms to the skillet and cook 5-6 minutes, stirring occasionally, until they release their liquid and begin to brown. This creates the foundation for your cozy fall skillet chicken mushroom's rich sauce.
Deglaze the pan with dry white wine, scraping up browned bits from the bottom. Add chicken broth, Dijon mustard, bay leaf, fresh thyme, and carrots. Return the browned chicken to the skillet.
Simmer for 8-10 minutes until the chicken is cooked through and carrots are tender. Remove from heat and stir in heavy cream until the sauce is silky and cohesive. Taste and adjust seasonings with additional salt and pepper as needed.