Preheat oven to 425°F. Place potatoes directly on oven rack, and bake until fork-tender, about 1 hour. Remove from oven, and let stand at room temperature until cool enough to handle, about 15 minutes. (Potatoes should still be hot.)

Meanwhile, melt butter in a small saucepan over medium. Add garlic, and cook, stirring often, until aromatic, about 2 minutes. Stir in milk, and cook until just warm, about 30 seconds. Remove from heat, and keep warm.

Cut potatoes in half lengthwise. Scoop out cooked potato from halves, leaving about ⅛ inch potato flesh on skin; place remaining cooked potato in a large bowl. Reserve 12 potato skins, and set aside. (Discard any remaining potato skins.)

Using a whisk or potato masher, whisk or mash cooked potatoes until smooth with no lumps, 1 to 2 minutes. Stir warm milk mixture, Parmesan, salt, and black pepper into potato mixture. Using a whisk, vigorously beat egg yolks, 1 at a time, into potato mixture until combined, scraping down sides of bowl as needed.

Brush outsides of reserved potato skins with oil, and place on a large rimmed baking sheet. Working in batches, transfer potato mixture to a piping bag fitted with a large open star tip. Pipe potato mixture into prepared potato skins in a decorative pattern, if desired.

Bake in preheated oven until piped potato mixture is lightly browned on top, 20 to 25 minutes. Remove from oven; garnish with black pepper, parsley, and flaky sea salt.