Step 1: Heat 2 tablespoons of olive oil in a large pot over medium heat.

Step 2: Add diced chicken breasts to the pot and cook until browned on all sides, about 5-7 minutes.

Step 3: Stir in finely chopped onion and minced garlic, cooking until the onion is soft and translucent, approximately 3-4 minutes.

Step 4: Pour in chicken broth and champagne, then add heavy cream, fresh thyme leaves, kosher salt, and freshly ground black pepper. Stir well to combine.

Step 5: Add sliced mushrooms to the pot and simmer for about 10 minutes until the mushrooms are tender.

Step 6: In a small bowl, mix all-purpose flour with a little bit of water to create a slurry. Stir the slurry into the soup to thicken it.

Step 7: Add tomato paste, a pinch of cayenne pepper (adjust to taste), diced shallots, and aged balsamic vinegar (if using). Stir to incorporate all the ingredients.

Step 8: Let the soup simmer for another 5-7 minutes, allowing all the flavors to meld together.

Step 9: Taste and adjust seasoning, adding more salt and pepper if needed.

Step 10: Once the soup is heated through and well blended, serve hot. Garnish with additional fresh thyme leaves if desired. Enjoy your delicious champagne chicken soup!