The key to success for a dish that has several moving parts is to take it one step at a time. To avoid any last-minute panic trying to serve the finished dish, set out bowls for the mussels and plates for the fries before you start cooking.
For the pommes frites
2 pounds large russet potatoes
Oil for frying
Kosher salt, to taste
For the mussels and the sauce
2 pounds live Mediterranean mussels in the shell
1/2 cup Pernod or other fennel-flavored aperitif
1 pint (2 cups) whipping cream, preferably organic
3 or 4 cloves of garlic, peeled and sliced thin
1 bulb of fresh fennel
1. Scrub the potatoes, peel them if desired, then slice them lengthwise into slabs, 3/8 inch thick. (It's best to use a mandoline-type slicer for this, but a good chef's knife and a steady hand will suffice.) Cut the slabs lengthwise into 3/8-inch batons. Hold the cut potatoes in cold water to rinse off some of the excess starch and prevent discoloration. Potatoes may be cut up to a day in advance if they are held in the refrigerator.
2. To prepare the mussels for cooking, rinse them under cold running water and snap off any dangling "beards" or hairy fibers; keep the mussels in a colander in the refrigerator until it's time to cook them. Mussels can be cleaned up to an hour before cooking.
3. To make the sauce, pour the Pernod into a deep, 4-quart, nonreactive saucepan over high heat and boil until the liquid is almost completely evaporated; add the cream and boil the liquid again until it is reduced to about half its original volume. The cream will expand as it boils, so stir it down if necessary to prevent it from boiling over. Meanwhile, split the fennel bulb in half lengthwise, trim off the leafy end and reserve a few of the prettier fronds to garnish the finished dish. Slice the bulb into 1/4-inch slices. Add the sliced fennel and garlic to the reduced cream and, after it returns to a boil, take it off the heat and keep it near the stove, ready for cooking the mussels.
4. To give the potatoes their first fry, preheat a countertop deep fryer to 325 degrees, or heat 8 cups of oil in a deep, heavy-bottomed Dutch oven until an instant-read thermometer registers 325. Line one sheet pan with a cooling rack to catch the cooked potatoes, and line a second sheet pan with a lint-free towel or a generous layer of paper toweling. Drain the potatoes and pat them completely dry with the paper towels. Fry the potatoes in several batches to avoid crowding the oil, stirring them to distribute evenly in the oil until they just begin to turn golden, about 4 to 5 minutes. Drain the par-cooked potatoes on the cooling rack and let them cool to room temperature, at least 10 minutes and up to an hour before serving time. To ready for the potatoes' second fry, raise the temperature of the oil to 375 degrees.
5. To cook the mussels, bring the sauce to a boil over high heat; add the mussels, cover the pan and cook until they are cooked through, about 7 minutes.
6. While the mussels are cooking, give the potatoes their second fry, about half the potatoes at a time, until golden brown and crisp, about 4 minutes. Drain, toss with kosher salt.
7. Serve the fries on plates and the mussels in bowls with their cooking liquid distributed evenly between them.
© Greg Atkinson, 2012