Heat oil and butter in a saucepan. Add onion and garlic and sauté over low-medium heat until tender (15 minutes). Add stock and bring to the boil, then add peas and bring back to the boil. Add mint, remove from heat and process mixture in batches in a blender until smooth. Stir through crème fraîche and lemon juice, season to taste and refrigerate until well chilled.
Meanwhile, for garlic croûtons, preheat oven to 180C. Place bread slices on an oven tray, brush both sides with olive oil and bake, turning once, until golden (5-10 minutes). Rub croûtons with the cut side of garlic, season to taste and cool. Croûtons will keep in an airtight container for 1 to 2 days.
Serve soup chilled with garlic croûtons, and an extra dollop of crème fraîche and cracked pepper, if you like.