Heat the olive oil in a dutch oven or large heavy-bottom saucepan over low heat. Add the onions and celery with a pinch of salt. Allow the vegetables to sweat for several minutes, stirring periodically, until softened. Add the squash and cook for several more minutes, stirring frequently.
Turn the heat up to medium and allow a brown glaze to slowly build on the bottom of the pan by stirring less often. Keep an eye on it to make sure it doesn't burn. Use a spatula to scrape up and incorporate the brown bits a few times. After several minutes, add the brandy to deglaze the pan and loosen the rest of the brown bits. Allow to alcohol to reduce down to almost nothing, stirring the vegetables frequently, and then add the thyme leaves and chicken stock.
Bring the liquid to a boil and then cover the pot and reduce the heat to low. Allow the soup to simmer for 1 hour.
Carefully transfer the soup to a blender and puree until very smooth. Wipe down the dutch oven and return the soup to the pot. Stir in the cream, salt and pepper.
Serve topped with spicy candied pecans.
Prepare the candied pecans:
Preheat the oven to 350 degrees F. Prepare a baking sheet by lining it with aluminum foil and spraying the foil with nonstick cooking spray.
Spread the pecans on the baking sheet and toast them in the oven until dark and fragrant, about 10 minutes. Stir every 3 or 4 minutes.
While the pecans are toasting, prepare the coating mixture. Microwave the butter in a large microwave-safe bowl until melted. Stir in the brown sugar, maple syrup, cinnamon, salt, and cayenne.
Once the pecans are fragrant, remove them from the oven and pour the hot nuts into the coating mixture. (Be careful as it might splutter and hiss.) Stir until the nuts are evenly coated, and pour them back onto the foil-lined baking sheet and spread them in an even layer.
Bake for another 10 minutes, stirring after every 3-4 minutes. After 10 minutes, remove the nuts from the oven and allow them to cool and crisp up on the baking sheet.
Once cool, break the nuts apart or chop them coarsely. Store Sweet and Spicy Candied Pecans in an airtight container at room temperature for up to a week.
You can save a ton of time with this recipe by using pre-peeled and diced squash. Candied pecans recipe reprinted with permission from Elizabeth LaBau at candy.about.com (originally adapted from David Lebovitz)