Roast garlic using your preferred method.
In a large pot over medium-low heat, add clarified butter and oil. When hot, add onions and garlic cloves; season with salt. Cook for 15 minutes, stirring frequently.
Add potatoes and season with freshly ground black pepper.
Stir in broth and bring the mixture to a boil. Reduce to medium and simmer for 15 minutes or until potatoes are tender.
Add roasted garlic, Herbes de Provence, hot paprika, salt, pepper, and lemon juice. Stir well and simmer gently for 5 minutes.
Pour in heavy cream, stir, and when the mixture simmers again, set the timer for 5 minutes.
Blend the ingredients until the mixture is smooth using an immersion blender. Add cooking sherry; taste and adjust seasoning if needed.
Spoon soup into warm bowls, add croutons and sprinkle on chopped parsley. Serve immediately.