1. Preheat the oven to 425.
2. Coat the squash in olive oil and season with 1 ½ tsp. Salt and ¾ tsp pepper. On a baking sheet lined with parchment paper, place the squash face down and roast until browned and tender (approximately 45 minutes to an hour). Once the squash is fully tender, allow it to cool completely before scooping out the inside of the squash. Place in a bowl and set aside.
3. Approximately 30 Minutes into roasting, start on the rest of the soup: In a small saucepan over low-medium heat add in the 1/2 cup of unsalted butter. Stirring or whisking constantly, cook butter until it is a deep golden brown and smells nutty. Set aside.
4. In a large heavy bottomed soup pot over medium high heat, add in 4 tbsp butter and 3 tbsp oil. Once the butter has melted and is starting to foam carefully add in the sliced onion and sliced fennel (approximately 8 minutes). Once the onion and fennel start to brown, reduce heat to medium and allow to cook until almost fully caramelized (about 10-12 minutes), stirring occasionally. Add in the apple and cook down until the apples are soft and have some caramelization (approximately 5 minutes).
5. Pour in the 6 cups of vegetable stock and bring to a simmer. Add in the roasted squash, spices, and season with a pinch of salt. Simmer for 10 minutes, then add in the heavy cream. Simmer for another 10 minutes. Carefully pour in the browned butter, stir, and turn heat off. (the butter should be cooled by now but if it is hot for any reason be careful as it can bubble up).
6. Using a ladle, carefully fill your blender with the soup mixture and blend on medium until completely smooth. Do this in batches if needed (I like using a blender because it achieves the consistency you want for the soup. A stick blender won’t do the job right.) Taste the soup for salt.
7. Serve with a drizzle of heavy cream, salted pepitas on top, and dried cranberries. Enjoy!