Step 1: Prepare the Onions

1. In a large skillet, heat 1 tablespoon of olive oil over medium heat.
2. Add the sliced onions and cook, stirring frequently, for about 15–20 minutes, until golden brown and caramelized.
3. Add the minced garlic, thyme, balsamic vinegar, salt, and pepper, and cook for an additional 2–3 minutes.
4. Remove from heat and let cool slightly.

Step 2: Prepare the Chicken

1. Preheat your oven to 375°F (190°C).
2. Slice a pocket into each chicken breast, being careful not to cut all the way through.

Step 3: Stuff the Chicken

1. In a bowl, combine the caramelized onion mixture with the shredded Swiss cheese and softened cream cheese until well mixed.
2. Spoon the filling into each chicken breast pocket, securing with toothpicks if necessary.

Step 4: Cook the Chicken

1. In the same skillet, heat the remaining tablespoon of olive oil over medium-high heat.
2. Add the stuffed chicken breasts and sear for 3–4 minutes on each side until golden brown.
3. Transfer the chicken to a baking dish and sprinkle breadcrumbs on top if desired.
4. Bake in the preheated oven for 20–25 minutes, until the chicken is cooked through and reaches an internal temperature of 165°F (74°C).

Step 5: Serve

1. Remove toothpicks if used and garnish with fresh parsley before serving.