Preheat the oven to 350ºF.

Bring the stock and salt to a simmer in a medium saucepan, then add the potatoes. They should be barely covered with stock; if not, add boiling water. Simmer gently, uncovered, until about three-quarters done, about 8 minutes. Drain, reserving the stock. Let the potatoes cool enough to handle.

Oil an 8-by-10-inch oval baking dish, or a baking dish of equivalent size. Working from the outside toward the center, arrange the potatoes in a ring of overlapping slices, inserting a tomato half after every 4 slices. Fill in the center of the ring with more potatoes and tomatoes. You may not need all the potatoes. Moisten with 1 cup of the reserved stock, drizzle with the olive oil, and season with pepper.

Bake until the potatoes absorb most of the liquid and begin to color on top, about 1 hour, rotating the dish halfway through. Let rest for a few minutes before serving.

Variation (from TV episode): Slice 4 cooked Italian sausages, pile in the center of the tart and heat for 10 minutes in the oven.