For roasted butternut squash:
Split the butternut squash in half lengthwise. Remove the seeds and brush the squash with 1 tablespoon of the olive oil. Sprinkle with ½ teaspoon of the kosher salt and ¼ teaspoon of the black pepper.
Place the squash with the cut side down on a rimmed baking sheet lined with foil and sprayed with a cooking spray. Roast the squash in a 400-degree oven for about 45 minutes or until the pieces of squash are cooked through and tender.
When cool it’s cool enough to handle, peel the squash and cut it into chunks. You should have about 9 to 10 cups of squash.
For the soup:
Place a large stockpot or Dutch oven over medium heat and melt the 3 tablespoons of butter with the remaining 3 tablespoons of olive oil. Add the chopped leeks and thyme and sauté until the leeks are tender, about 12 minutes, stirring occasionally. Add the chopped garlic and cook for an additional 3 minutes.
Add the roasted squash and pour in the chicken stock. Add the concentrated chicken base, the remaining ½ teaspoon of kosher salt and ¼ teaspoon of black pepper.
Bring the stock to a boil over medium heat, then partially cover the pan, reduce the heat to medium-low and simmer for 20 minutes.
Using an immersion blender purée the soup until it’s smooth.
Stir in the half and half and cook for an additional 5 to 10 minutes to heat through.
Serve with grated Parmesan cheese.