Add extra virgin olive oil to a large heated pan. Sauté mushrooms until golden brown. Add onions, garlic and thyme sauté until the onions are soft. Mix brown gravy mix and chicken base with the water. Add mixture to sautéed veggies. Add brandy and let simmer. Add a little more water if need to ensure a creamy consistency. Add cream and simmer. Let sauce reduce by half.
In a large bowl, combine chicken, olive oil, greek seasoning, garlic cloves and lemon zest. Marinate for at least 2 hours. On a hot grill cook chicken for 12-15 minutes. Turn once. Internal temperture should read 160 degrees.
Preheat oven to 375 degrees. Combine all ingredients for the roasted broccoli. On a large baking sheet arrange broccoli in a single layer. Roast for 10-15 minutes, or until broccoli florets are golden brown. Turn once.