Cut the garlic heads across, about a quarter of the way down from the top of the cloves. Remove the outer skin. Spoon 4 tsp. of the olive oil on four puddles on a clean (preferably stainless steel) pan. Put the pan in the oven and bake for an hour and fifteen minutes. Remove, cool, and peel all the garlic.
Move the pan to a medium-hot burner on the stove. Add the remaining olive oil, leeks, celery, and the garlic. Cook until everything is soft. Add the wine and bring it to a boil for about a minute.
Add the chicken stock and the potatoes, and bring to a boil. Reduce to a simmer and cook for about an hour and 15 minutes.
Strain the soup and puree the solids in a food processor, along with enough broth to makes it smooth. Strain the puree through a medium sieve back into the soup. Return to a simmer. Add the whipping cream, thyme, salt, pepper and Tabasco.
Right before you're ready to serve, heat the extra virgin olive oil in a skillet over high heat. Add the the slivers of garlic and sizzle them until browned around the edges.
Right before you're ready to serve, heat the extra virgin olive oil in a skillet over high heat. Add the the slivers of garlic and sizzle them until browned around the edges.
Ladle the soup into bowls and garnish with the toasted garlic slivers.
