Preheat oven to 400°F. Place red bell peppers, cut side down, on a foil lined baking sheet and roast for 30 to 40 minutes until skins are wrinkled and charred.
Place roasted peppers in a plastic zip top bag or covered bowl to steam for 15 minutes. Remove, peel off skins and slice thinly.
Heat olive oil in a large stockpot over medium-high heat. Add leeks, potatoes, and cauliflower; cook, stirring often, for 8 to 10 minutes until softened. Season with salt and pepper.
Pour in vegetable stock and bring to a boil. Reduce heat and simmer for 30 minutes until vegetables are tender. Remove from heat.
Heat a glug of olive oil in a sauté pan over medium-high heat. Add mushrooms and sauté for 5 to 6 minutes until tender. Season with salt.
Puree the soup using an immersion blender or standard blender in batches until smooth. Stir in lactose-free milk and mix well. Season with salt and pepper to taste.
Serve soup in bowls topped with sautéed mushrooms, roasted red bell pepper strips, fresh chives, and shaved Parmesan cheese. Enjoy your comforting Velvety Leek & Potato Soup.