Set a heavy-bottomed soup pot over medium heat. Melt butter, add fennel and leeks, and turn heat to medium-low. Cook, stirring often, until fennel and leeks are tender and translucent – about 20 - 30 minutes. Vegetables should be cooked thoroughly, but not at all browned – edge heat lower as needed.

Add potatoes, bay leaves, broth, and a generous pinch of sea salt. Bring to a boil, then turn down to simmer until potatoes are fork tender, 20 - 30 minutes more.

Use tongs to remove potato chunks, and push through a ricer or food mill. Carefully puree the remaining soup in a blender. (Always use caution when blending hot soup. Divide soup in to batches if your blender is small.) Return riced potatoes and blended soup to the pot. Warm soup over medium-low heat. Add sea salt and black pepper to taste. Finally, stir in the milk and lemon juice.

Serve soup with minced fennel fronds, chives, and a twist of freshly ground black pepper.