-Melt 2 TBS butter with 2 TBS olive oil in a large, heavy pot.

-Add 2 thinly sliced fennel bulbs also thinly sliced.

-Cover and cook until fennel is tender, about 15 minutes.

-Add 1 pound potatoes, peeled and diced into small chunks.

-Add 4 cups chicken or vegetable broth and simmer until potatoes are very tender, about 30 minutes.

-Remove from heat and add 2 TBS Pernod or Calvados.

-Season with sea salt and freshly ground black pepper.

-Working in small batches, puree soup in the blender.

-Transfer it all to a bowl and add 2 cups half-and-half.

-Taste for salt and pepper.

-Chill for a few hours and serve cold with a sprinkle of chopped basil or dill.