Cut each potato lengthwise into 8 wedges. You should have 32 potato pieces. (like joe joes).
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; Combine garlic, olive oil, lemon juice, zest and oregano in a small bowl, pour over potatoes and stir well.
Cook on second side, about 5 minutes longer. Stirring once more, add ground black pepper and reduce heat to medium-low, cover tightly, and cook until potatoes are tender when pierced with tip of paring knife, about 5 minutes.
Sprinkle with parsley, stir gently to distribute; serve immediately. (optional - add 3 oz crumbled feta and 8 Kalamata olives (sliced thin) and add in with the parsley.