Preheat the oven to 400°F and line a baking sheet with parchment paper.

Slice the squash in half lengthwise and scoop out the seeds. Drizzle the squash halves with olive oil and sprinkle with salt and pepper. Place cut side down on the baking sheet. Wrap the garlic cloves in a piece of foil with a drizzle of oil and a pinch of salt and place on the baking sheet, along with the peeled and cut carrots and tomato. Roast for 35 to 45 minutes, or until the squash is tender when pierced with a fork. Remove from the oven and set aside to cool.

When cool enough to handle, peel the garlic cloves and discard the papers. Scoop the soft squash flesh out of the skin and measure 2½ cups. Discard the squash skins and save the remaining flesh for another use.

Heat the olive oil in a large pot or Dutch oven over medium heat. Add the onion and salt and cook, stirring occasionally, for 5 to 8 minutes, or until softened. Stir in the nutmeg, cayenne, and several grinds of pepper, then add the 2½ cups roasted squash, the garlic, carrots, tomato, broth, and thyme leaves. Simmer, stirring occasionally, for 20 minutes.

Allow the soup to cool slightly, add the lemon juice and maple syrup and blend (with an immersion or traditional blender) until smooth. Work in batches if necessary. Season to taste. Add heavy cream if desired.

Portion into bowls and garnish with chives and/or Parmesan cheese if desired.