Preheat oven to 425 degrees F. Melt butter in saucepan set over medium heat; cook half of the leeks and 1/4 tsp. each salt and pepper for 8 to 10 minutes or until lightly golden brown and tender.
Stir in broth, potatoes, thyme, and bay leaves; bring to boil. Reduce heat to medium-low; cook for 15 to 18 minutes or until potatoes are tender. Remove thyme and bay leaves. Stir in cream; cook for 1 to 2 minutes or until heated through. Using hand blender, puree until smooth. Stir in lemon juice and nutmeg.
Pat remaining leeks dry with paper towel; toss with oil. Sprinkle with flour and remaining salt; toss until evenly coated. Arrange in single layer on parchment paper–lined baking sheet. Bake, turning once, for 8 to 10 minutes or until golden brown. Let cool completely.
Divide soup among 4 bowls. Top with crispy leeks, chives, and remaining pepper.
Alternatively, transfer soup to stand blender; puree in small batches, placing tea towel over lid, until smooth.
To serve cold, let cool completely and refrigerate before serving.