Prepare Leeks: slice off root tip and save white-part plus 1-inch of green. Split in half, wash well (grit will ruin a dish) and pat dry. Cut leeks into thin slices, either by hand or with the medium (4mm) slicing disk of a food processor. Heat a medium saucepan over moderate heat and add 2 tbsp butter. Add leeks and cook, stirring, for 2 minutes. Cover and continue to cook for 20 minutes. Be careful not to brown leeks. Stir cream into leeks and boil about 3 minutes until thickened. Season with salt and pepper.
Prepare Potatoes: Peel potatoes and cut in half to fit a food processor's feed tube. using the julienne blade, cut potatoes into julienne strips. If doing by hand, cut potatoes into thin matchsticks. Rinse potatoes in several changes of cold water to remove any starch. Drain well and then spread out potatoes on a kitchen towel then roll up the to towel to squeeze out as much moisture as possible.
Assemble Cake: About 30 minutes before serving, heat the clarified butter over medium heat in a large nonstick skillet. Spread half the potatoes over the bottom of the pan, smoothing them to the edges. Top with creamed leeks spread to within 1 inch of the edge. Cover with remaining potatoes and pat then down to form a tight cake about 10 inches in diameter.
Cook Cake: Cover and cook over medium heat, shaking the pan frequently to keep potatoes from sticking to the pan. After 5 minutes, lift off cover to let the steam escape. Wipe down cover and put it back on the pan to cook for another 5 minutes. Shake pan occasionally to keep the potato cake from sticking to the bottom of pan.
Remove cover, being careful no to drip any moisture back into the pan. Wipe the cover dry again. Tilt pan and spoon off any excess butter into a bowl. Shake pan to be sure potatoes aren't sticking to the bottom Cover pan with lid but this time, flip pan with lid so that potato cake is resting on the lid soft-side down. Add reserved butter back to pan, heat, and then carefully slide the potato cake off the lid and back into the pan to crisp the other side. Continue cooking, uncovered, over medium-low heat until bottom becomes golden brown, 10-15 minutes. Slide onto dish, salt and pepper, and serve immediately.