Preheat oven broiler and place rack in highest position. Grease baking sheet with olive oil.
Cut peppers in half and remove stems and seeds. Place cut side down on baking sheet. Lightly brush with olive oil. Broil until skins blacken, about 8 minutes. Transfer to bowl and tightly seal to steam. Set aside until peppers are cool enough to handle.
Alternatively, broil whole peppers on a barbecue, turning them with long-handled tongs until peppers are blackened and blistered. Place in bowl and tightly seal to steam and cool.
In large heavy saucepan, heat oil. Add onion, celery, and carrot, and sauté until onion is clear. Add potato, garlic, thyme, and bay leaf, and sauté for a minute. Add stock and paprika and bring to a gentle boil. Cover, reduce heat, and simmer until potato is fork-tender.
While potato is cooking, peel skin from peppers; chop peppers, and place in bowl. Add any juices that may have collected. When potato is tender, remove bay leaf. Add roasted peppers and any juices that may have collected to saucepan with potatoes. Stir together.
Transfer mixture to high-speed blender and purée until smooth and creamy. Alternatively, purée using hand-held stick blender. Return to saucepan and heat through just until piping hot. Add a splash of lemon, if you wish.
In bowl, stir together gremolata ingredients. Serve soup with gremolata scattered overtop. Dot with hot chili oil, if you wish. Serve with a smattering of finely diced croutons as an option.