Cut a slit along the length of the leeks and run under cold water, fanning out the layers to clean away dirt and grit. Finely dice. Core and finely dice fennel bulb.
Heat butter and olive oil over medium heat in a large soup pot and add leeks, fennel and a big pinch of salt. Cook, stirring occasionally until quite soft and starting to caramelize.
While leeks and fennel are cooking you can peel, quarter, and thinly slice russet potatoes. Put potatoes on a bowl of water as you prep them to keep them from browning.
Drain potatoes and add them to the pot along with 1/2 cup parsley, bay leaf and 6 cups chicken or vegetable stock. Bring to a boil, reduce to a simmer and cook until potatoes are falling apart.
Add cream and stir to heat through. Blend soup either partially or completely. Thin with more chicken stock if necessary and stir in remaining 1/4 cup chopped parsley.