Preheat the oven to 450°F (230°C).
Using a sharp knife, carefully slice each potato into thin, ¼-inch sections, cutting down along the potato from one end to the other but stopping before you reach the bottom. Leave about ¼-inch of the potato uncut to hold it together. For assistance, you can place chopsticks on either side of the potato to prevent slicing all the way through, especially in the middle sections. For the ends, proceed slowly with a gentle, careful sawing motion to ensure the cuts don’t go all the way through. Repeat this with all the potatoes.
In a small bowl, whisk together the olive oil, melted vegan butter, garlic, rosemary, salt, and black pepper. Generously brush half of this mixture over the potatoes, making an effort to get the seasoning between each slice.
Place the potatoes in the oven, uncovered, and bake for 30 minutes. Take them out, then brush them again with the remaining garlic and olive oil mixture, ensuring it seeps between the slices. Return the potatoes to the oven and continue baking for another 25 to 30 minutes, or until they are tender inside and golden crisp on the outside.
Serve the potatoes warm, garnished with fresh parsley. Leftover potatoes can be stored in the fridge in a covered container for 3 to 4 days. Enjoy them cold, or reheat in the microwave, air fryer, or oven for best results.