Preheat your oven to 400˚F.
Cut the top off the garlic to reveal the cloves. Drizzle with olive oil, sprinkle with salt, then wrap in aluminum foil and roast for 40 minutes.
While the garlic works its magic in the oven, peel and halve or quarter your potatoes. Add them to a pot of cold, salted water. Bring it to a boil, then simmer for 15 minutes until the potatoes are fork-tender but not mushy.
Drain the potatoes in a colander, breaking them into smaller pieces to release more steam. We want them as dry as possible.
In a pan over medium-low heat, rice your potatoes and roasted garlic. Stir in cheese, butter, salt, and pepper. Taste and adjust, then turn off the heat and add the egg yolks. The potatoes should form a smooth dough.
Cover the potatoes with plastic wrap to prevent a skin from forming. Let them cool until they’re cool enough to handle.
Pipe the mixture into swirls on a parchment-lined baking sheet. Brush with a touch of melted butter (not too much), and bake for 20 minutes at 400F, until the edges and bottoms are golden brown.
Now, savor the crispy, buttery goodness. Enjoy!