Preheat the oven to 400 degrees F (200 degrees C).
Fill a large bowl with cold water and stir in lemon juice; set aside.
Slice off the bottom of a potato lengthwise to make it steadier for cutting. Place potato between two chopsticks. Cut slits 1/4 inch apart, using the chopsticks as a guide to keep from cutting all the way through; the slices should stay connected at the bottom. Carefully fan out the sliced pieces without breaking them apart. Place cut potato in the prepared water bowl while you cut remaining potatoes.
Melt butter in a saucepan over medium heat. Turn off the heat. Stir in rosemary sprigs, garlic, salt, and pepper. Let sit until flavors meld, 2 to 3 minutes.
Remove potatoes from water, dry thoroughly, and place on a baking sheet. Brush potatoes with some of the butter mixture.
Bake potatoes in the preheated oven for 30 minutes. Brush with more butter mixture, ensuring butter flows down fanned potato slices. Continue baking until potatoes are tender and crisp, about 30 minutes more.
Remove potatoes from the oven and brush them with remaining butter mixture. Sprinkle with salt and garnish with parsley. Serve hot.