Either remove a strip of the peel around the center of each potato or cut the potatoes in half. Place in a saucepan. Nearly cover with the broth of your choice. Bring to a boil, add a lid and turn down to a good simmer. Cook for 15 to 20 minutes, until potatoes are just tender.
Remove lid and continue to simmer until potatoes are soft and broth is reduced, turning the potatoes from top to bottom now and then. Once tender, tender, the broth should have reduced to almost a glaze. Remove from heat, add butter and parsley, toss and place potatoes in serving dish. Sprinkle with salt, if desired.
Note: These potatoes are literally cooked in broth, so it won’t ever be thick like a “gravy” but should end up like a “glaze.”