Preheat the oven to 425 degrees F. Lightly coat a shallow 3-quart baking dish with nonstick cooking spray and set aside.
Equip the food processor with the slicing disk (the thin slicing disk, if you have one). Stand as many pieces of potato in the feed tube as will fit, then exerting gentle pressure on the pusher, pulse the potatoes through the slicing disk. Repeat until all the potatoes have been sliced. As the work bowl fills, scoop the potatoes onto a large piece of waxed paper. Scoop the last batch of sliced potatoes onto the waxed paper and reserve.
Slice the onions just as you did the potatoes, transfer to a second sheet of waxed paper, and reserve. Remove the slicing disk from the processor and insert the chopping blade.
Add the anchovy paste, butter, flour, pepper, and 1/2 cup of the cream to the processor and churn 3 to 5 seconds until smooth. Add the remaining cream and the milk and pulse 4 to 5 times to incorporate.
Layer 1/3 of the potatoes in the prepared casserole, spreading evenly, top with 1/3 of the onions and 1/3 of the anchovy mixture. Repeat twice. The anchovy mixture should just be visible in the casserole; it should not cover the onions and potatoes.
Bake uncovered on the middle oven rack until bubbling and nicely browned, about 1 hour. Remove from the oven and let stand 10 minutes before serving.
If your food processor has a thin slicing disk, by all means use it. Otherwise, the medium disk will do. Also, because of the saltiness of the anchovy paste, this recipe needs no salt.
Recipe courtesy Jean Anderson, Process This, William Morrow, 2002