Preheat your oven to 400 degrees Fahrenheit.
Whisk the olive oil, lemon juice, vegetable broth, minced garlic, dried oregano, salt, and pepper in a large bowl.
Toss the potato wedges in the liquid mixture until fully coated.
Arrange the potatoes and all the liquid in a single layer inside a large metal baking dish.
Bake for 45 to 50 minutes, flipping the potatoes carefully halfway through, until fork-tender and the liquid has absorbed.
Garnish immediately out of the oven with the crumbled feta cheese and fresh chopped parsley. Serve warm.