1. Heat vegetable oil and butter in heavy-bottomed 12-inch nonstick skillet over medium-high heat until butter melts and foaming subsides, swirling pan occasionally. Add potatoes in single layer; cook until golden brown (pan should sizzle but not smoke), about 6 minutes. Using tongs, turn potatoes so second cut sides are down; cook until deep golden brown on second side, about 5 minutes longer. Reduce heat to medium-low, cover tightly, and cook until potatoes are tender when pierced with tip of paring knife, about 5 minutes.

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2. While potatoes cook, combine garlic, olive oil, lemon juice and zest, and oregano in small bowl. When potatoes are tender, add garlic-lemon mixture, salt, and pepper; stir carefully (so as not to break potato wedges) to distribute. Cook, uncovered, until seasoning mixture is heated through and fragrant, 1 to 2 minutes. Sprinkle potatoes with parsley, stir gently to distribute; serve immediately.