Trim away the finocchio tops down to the bulb. Pull off and discard any bruised, discolored outer leaf. Cut the finocchio lengthwise into ¼-inch-thick slices. If parts of the finocchio separate from the slice do not worry, it is still usable.
Wash the finocchio in 2 or 3 changes of cold water, shake dry, and place flat in the baking pan. Add the butter and oil and sprinkle with salt. Put the pan in the uppermost level of the preheated oven.
Turn the finocchio over after about 10 minutes. Continue baking until halfway done. Depending on the freshness of the finocchio, it may take another 5 to 10 minutes: When pricked with a fork it should feel firm and somewhat resistant.
Add the potatoes, tossing them well with the finocchio to separate all the potato slices. Sprinkle with salt and add a few grindings of pepper. Return to the oven. Bake until the potatoes are tender, about 25 to 30 minutes, and the finocchio has become colored a light nut brown. Turn and baste the finocchio and potatoes every/ 8 to 10 minutes. Serve after allowing the dish to settle briefly out of the oven.