Preheat the oven to 340°F (170°C).
Wash the potatoes and cut them into evenly sized chunks (about 1–1.5 inches); leave the skins on.
In a large rimmed baking sheet or in a mixing bowl, combine the olive oil, lemon juice, broth (vegetable or chicken), lemon zest, sliced garlic cloves, dried oregano, and salt. Stir or whisk until the ingredients are evenly mixed.
Add the potato chunks to the baking sheet or bowl and toss gently so all pieces are evenly coated with the lemon–oil mixture. If you mixed in a bowl, transfer the coated potatoes to a single layer in a rimmed baking sheet.
Cover the baking sheet tightly with aluminum foil, sealing the edges to trap steam.
Roast in the preheated oven, covered, for 70 minutes.
Remove the baking sheet from the oven and carefully lift off the foil (watch for steam). Gently turn the potatoes with a spatula or tongs so they brown evenly.
Return the pan to the oven uncovered and roast for an additional 10 minutes.
The potatoes are done when they are tender when pierced with a fork, lightly golden, and most of the liquid has reduced. Remove from the oven and serve.