Garlic Soup With Potatoes and Poached Eggs

Heat 2 Tbsp. oil and 2 Tbsp. butter in a large saucepan over medium. Add garlic, white and pale green parts of leek, and thyme and cook, stirring often, until garlic is softened, about 5 minutes (reduce heat if garlic starts to brown). Add potatoes and 4 cups broth, bring to a simmer, and cook until potatoes are very tender, 25–30 minutes. Let cool slightly, then add crème fraîche.

Transfer soup to a blender (or use an immersion blender directly in saucepan) and blend until very smooth; season with salt and pepper. Transfer soup back to saucepan and set aside.

Pour water into another large saucepan to come 4" up sides and bring to a boil, then reduce heat so water is at a gentle simmer. Crack an egg into a small bowl, then gently slide egg into water. Repeat with remaining eggs, waiting until whites are opaque before adding the next one (about 30 seconds apart). Poach until whites are set but yolks are still runny, about 3 minutes. Using a slotted spoon, transfer eggs to paper towels as they are done; season with salt and pepper.