Position a rack in the center of the oven and heat the oven to 400ºF. Line a heavy-duty rimmed baking sheet with parchment.
In a mortar and pestle, pound the oil, garlic, coriander seeds, fennel seeds, and sage until they resemble a coarse paste. Rub the spice mixture on the flesh of the squash halves. Set them cut side down on the prepared pan and roast until tender when pierced with a fork, about 1 hour. Let cool, cut side up. When cool enough to handle, scrape the flesh away from the rind—you’ll need about 5 cups.
Melt the butter in a 5- to 6-quart Dutch oven over medium heat. Add the leek, carrots, and a big pinch of salt and cook, stirring occasionally, until the leek is softened, 8 to 10 minutes. Add the squash, broth, bay leaf, and 1 tsp. salt and bring to a boil over high heat. Reduce the heat to a low simmer, cover, and cook for 30 minutes to develop the soup’s flavor.
Remove the bay leaf and allow the soup to cool slightly. Purée the soup in batches in a blender. Return the soup to the pot and add the lemon juice. Season to taste with salt and pepper. Garnish with the chopped hazelnuts, chives, and Espelette pepper or cayenne.