Preheat the Oven: Set your oven to 400°F and prepare a 9×13-inch baking dish.
Roast the Onions and Garlic: In the baking dish, add the sliced onions, chopped sun-dried tomatoes, balsamic vinegar, salt, paprika, and Italian herbs. Toss everything together to coat well. Place the garlic head (cut side up) in the center of the dish and drizzle generously with olive oil. Cover tightly with foil and roast for 1 hour, stirring halfway through, until the onions are caramelized and soft.
Cook the Chicken: While the vegetables roast, pat the chicken strips dry with paper towels. In a bowl, season them with garlic powder, onion powder, and a pinch of salt. Heat a large skillet over medium-high heat and drizzle with olive oil. Working in batches, sear the chicken for 3 to 4 minutes per side until golden brown and cooked through. Remove from heat and set aside.
Blend the Flavors: Once the roasted onions and garlic are ready, remove the baking dish from the oven. When the garlic has cooled slightly, squeeze the roasted cloves out of their skins into the dish. Stir in the heavy cream and fresh parsley, then add the seared chicken strips. Mix everything gently until the chicken is fully coated in the creamy balsamic sauce.
Finish and Serve: Place the baking dish back in the oven for 5 minutes to let the flavors meld. Remove and serve warm, spooning extra sauce over each portion.
