Peel 1 1/2 pounds thin-skinned potatoes and cut into 1/8- to 1/4-inch-thick slices. Cover the bottom of a shallow 1 1/2-quart casserole with half the potato slices.
Trim and discard stalks from 1 head fennel (about 3 in. wide), saving feathery green tops. Trim and discard any bruises and coarse fibers from fennel head, then rinse and thinly slice, using a hand slicer or food processor.
Discard casing from about 2 ounces dried salami. Cut meat into thin slices, then cut slices into slivers.
Mix half the salami with the sliced fennel and arrange evenly over potatoes in casserole. Cover with remaining potato slices. Add 1 cup fat-skimmed chicken broth. Cover casserole tightly with foil.
Bake in a 375° oven until potatoes are tender when pierced, 1 hour to 1 hour and 10 minutes (45 to 55 minutes in a convection oven). Uncover, sprinkle with 1/3 cup finely shredded parmesan cheese, and bake 5 minutes longer.
Finely chop fennel tops, mix 2 tablespoons (save rest for other uses) with remaining salami, and sprinkle over casserole. Add salt and pepper to taste.