Preheat the oven to 400°F. To roast whole chestnuts, make an “X”-shape cut into each chestnut with a small serrated knife, making sure to slice deeply enough past the shell. Place the chestnuts on a baking tray and roast in the oven for 15-20 minutes. The “X” in the chestnuts should start to open and peel back slightly. Let cool for a bit, then peel off the shells and chop roughly.
In a food processor or high-powered blender, add the chestnuts, chopped carrots, and the non-dairy milk. Blend until smooth and creamy. Set aside.
In a large non-stick pot add the leek and garlic and cook on medium heat for 10 minutes, until fragrant and the leeks have softened. Add the carrot-chestnut blend, turmeric, paprika, thyme, and vegetable broth and cook for 25-30 minutes over medium heat, or until soup is creamy. Serve sprinkled with pepper and thyme.