Step 1Heat the oven to 400 degrees. Place the garlic in a small bowl with the olive oil and set aside.
Step 2Heat 2 tablespoons of the butter in a large sauce pot until melted. Add the celery, carrots and onion and saute over medium-low heat until tender, about 10 minutes, stirring occasionally. Add the minced garlic and saute until fragrant, about 1 minute.
Step 3Add the squash to the pot. Stir in the chicken broth and bring the mixture to a boil. Reduce the heat and simmer 45 minutes to 1 hour, until the squash is tender.
Step 4While the soup simmers, make croutons by cutting the bread slices into 12 (half-inch by 4-inches) strips. Brush the cut sides of the bread with the garlic-infused oil. Place on a baking sheet and bake 12 to 15 minutes, until lightly browned. Set aside.
Step 5When the squash is tender, puree the soup in a blender or food processor, in batches if necessary. Return the soup to the pot. Add the remaining butter, bit by bit, to the soup, swirling until each piece is incorporated and the soup is slightly thickened. Season with salt and pepper.
Step 6To serve, spoon about three-fourths cup soup into each of 6 soup bowls. Top each with a dollop of sour cream and a pinch of piment d'espelette. Sprinkle parsley over the croutons, then place 2 croutons on top. Serve immediately.