Melt butter in a large stock pot. When melted, stir in leeks and garlic until well coated. Sprinkle with a bit of kosher salt. Reduce heat to low, cover, and cook, stirring once or twice, for 10 minutes, or until soft.
Add remaining ingredients, along with a bit more salt and pepper, then increase the heat and bring to a boil.
Once bubbling, reduce heat to low and simmer, mostly covered, until all vegetables are soft, 30 to 40 minutes.
Taste and season with salt and pepper.
Working in batches, puree soup in a blender until smooth. Return to the pan and heat as needed.
Serve topped with croutons and chervil.