Season chicken breasts generously with salt, pepper, and paprika. Pound them to even thickness for uniform cooking. Heat olive oil and butter in a large oven-safe skillet over medium-high heat until the butter foams and subsides.

Add chicken to the hot skillet and sear for 4-5 minutes per side until golden brown. The chicken doesn't need to cook through completely. Transfer chicken to a plate and set aside.

In the same skillet, add diced onion and cook for 3-4 minutes until softened and fragrant. Add minced garlic and thyme, stirring for another 30 seconds until aromatic. Sprinkle flour over the vegetables and stir constantly for 1 minute to eliminate the raw flour taste.

Slowly pour in chicken broth while whisking continuously to prevent lumps. Add heavy cream and bring the mixture to a gentle simmer. The sauce should coat the back of a spoon. Remove from heat and gradually stir in shredded Swiss cheese until melted and smooth.

Return chicken to the skillet, nestling it into the creamy sauce. Transfer to a preheated 375°F oven and bake for 12-15 minutes until chicken reaches 165°F internal temperature. Let rest for 5 minutes before serving to allow the sauce to thicken slightly.