Combine oil and onions in a pot over low heat. Cover and cook until very tender and soft, 30 to 40 minutes. Remove cover and sprinkle sugar over onions. Cook, uncovered, until onions are light brown, 10 to 15 minutes more.

Stir Brussels sprouts and thyme into the pot. Pour in stock and season soup with salt and pepper. Bring to a boil, reduce heat, and simmer until sprouts are just tender, about 10 minutes.

Allow soup to cool slightly. Blend to a smooth consistency using an immersion blender. Reheat gently, about 2 minutes, and adjust seasoning if necessary.

Top each portion of soup with a spoonful of sour cream and a dash of hot pepper sauce.