Heat 1 tablespoon olive oil in a medium saucepan over medium heat. Add the smashed garlic and onion and cook, stirring, until soft and lightly golden, about 8 minutes. Add the wine, thyme, bay leaf, 1/2 teaspoon salt, pepper to taste and the cheese rind. Bring to a simmer and cook until reduced by half, about 5 minutes. Add 5 cups water, reduce the heat to low and bring to a gentle simmer; cook until the garlic is very soft, about 30 minutes. Remove from the heat, add the bread and let soak, 10 minutes.
Remove the thyme, bay leaf and cheese rind from the saucepan; stir in the grated cheese, sour cream and 1/2 teaspoon salt. Transfer the soup to a blender in batches and puree until smooth. Season with salt and pepper.
Combine the remaining 3 tablespoons olive oil, the sliced garlic and a pinch of salt in a skillet over low heat; cook until the garlic is golden and crisp, 12 to 15 minutes.
Divide the soup among bowls. Top with the fried garlic, some of the garlic oil, and dill.
Photograph by Christina Holmes
When blending hot liquids, first let cool for 5 minutes or so, then transfer to a blender, filling only halfway. Put the lid on, leaving one corner open; Cover the lid with a kitchen towel to catch splatters and pulse until smooth.
Recipe courtesy Food Network Magazine