In a medium Dutch oven, melt 3 tablespoons butter over medium heat. Add leek, 2 teaspoons garlic, and thyme; cover and cook over medium-low heat until leek is softened but not browned, about 20 minutes.
Add potatoes, chicken stock, 2 teaspoons salt, and black pepper; bring to a boil over medium-high heat. Reduce heat to medium-low; partially cover and cook until potatoes are tender, about 25 minutes. Remove from heat; let stand until slightly cooled.
In a large sauté pan, heat remaining 1 tablespoon butter over medium-high heat. Add crawfish, and cook until golden brown; turn crawfish. Add shallot and remaining 1 teaspoon garlic; cook until shallot is slightly softened, about 1 minute. Add wine; cook until slightly reduced, about 2 minutes.
Add Creole seasoning, lemon juice, and red pepper; cook just until heated through. Add 1 cup sautéed crawfish to soup, coarsely chopping the remaining crawfish for garnish.
In the container of a blender, working in batches, if necessary, process soup until smooth. Return soup to pot, and stir in cream and remaining ½ teaspoon salt. Cook over medium-low heat until heated through. Garnish with cream, chives, lemon zest, and remaining sautéed crawfish, if desired.
Recipe by Louisiana Cookin' at https://louisianacookin.com/crawfish-cream-of-leek-soup/