Season both sides of the chicken breasts with salt and black pepper.
Heat olive oil in a large skillet over medium-high heat. Add the chicken breasts and cook for 5-6 minutes on each side until golden brown and cooked through. Remove chicken from skillet and set aside.
Reduce heat to medium. Add the butter to the same skillet. Once melted, add the sliced onions and cook, stirring occasionally, for about 15 minutes until deeply caramelized and golden brown.
Add the minced garlic, dried thyme, and smoked paprika to the onions. Cook for 1 minute until fragrant.
Sprinkle the flour over the onions and stir well to combine. Cook for 1-2 minutes to remove the raw flour taste.
Slowly pour in the beef broth while stirring to prevent lumps. Bring the mixture to a simmer and cook for 3-4 minutes until slightly thickened.
Stir in the heavy cream and half of the shredded Gruyère cheese. Cook until the cheese melts and the sauce is creamy, about 2 minutes.
Return the cooked chicken breasts to the skillet, nestling them into the sauce. Sprinkle the remaining Gruyère cheese evenly over the chicken.
Cover the skillet with a lid and cook for 3-4 minutes on low heat until the cheese is melted and bubbly.
Remove from heat and garnish with chopped fresh parsley before serving.