Heat 3 tablespoons olive oil in a large skillet over medium-high heat. Once shimmering, season chicken pieces with salt and paprika, then sear for 4-5 minutes per side until golden brown. Transfer to a plate and set aside—it doesn't need to be fully cooked yet.
In the same skillet, add 2 tablespoons butter and sauté the diced onion for 3 minutes until softened. Add minced garlic and cook for 1 minute until fragrant, stirring constantly to prevent burning.
Add your sliced mushrooms to the skillet and cook for 5-7 minutes, stirring occasionally until they release their moisture and begin browning. This step builds the umami foundation that makes this chicken mushroom skillet truly special.
Return the seared chicken to the skillet along with baby potatoes, sliced carrots, and the bay leaf. Pour in 2 cups chicken broth and bring to a simmer for 15 minutes until vegetables are tender and chicken is nearly cooked through.
Stir in 1 cup heavy cream, 2 tablespoons fresh thyme, and 1 tablespoon Dijon mustard. Whisk cornstarch with 2 tablespoons water to create a slurry, then stir it into the cozy chicken mushroom skillet for 2-3 minutes until the sauce thickens beautifully and coats a spoon.
Taste and adjust seasoning with additional salt and pepper as needed. Simmer for 5 more minutes to marry all flavors, then remove the bay leaf and serve immediately while the sauce is silky and warm.