Time: 2 hours

12 whole peeled garlic cloves, plus 1 tablespoon minced
1 cup sweet Spanish sherry
3 1/2 pounds russet potatoes (about 7 medium), peeled
2 cups or more extra virgin olive oil
Salt and freshly ground black pepper
1 large Spanish onion, diced
12 eggs plus 2 yolks
3 tablespoons chopped flat-leaf parsley
3 tablespoons sherry vinegar.

1. Heat oven to 375 degrees. Combine garlic cloves and sherry in a small saucepan, and place over medium heat. Simmer until syrup forms and garlic is soft, about 40 minutes. Cool to room temperature.

2. While garlic is simmering, thinly slice potatoes, with a mandoline preferably. In a large mixing bowl, toss potatoes with about  1/4 cup olive oil and season liberally with salt and pepper. Spread potatoes on a pan over parchment paper, bake 18 minutes, and remove from oven to cool.

3. Place a large skillet over medium heat and sauté onions with 2 tablespoons olive oil until translucent, about 3 minutes. Coat a 10- or 12-inch round Teflon frying pan with olive oil. In a large mixing bowl, beat 12 eggs, parsley and minced garlic. Add potatoes and onions, stir to combine, and transfer mixture — arranging potatoes in horizontal layers — to frying pan.

4. Place pan uncovered over low heat until eggs are set, about 40 minutes. Carefully loosen tortilla from sides and bottom of pan with a rubber spatula. Hold a plate over the pan with one hand, grasp pan handle with the other, then flip; the tortilla should easily fall onto the plate. (If it does not, use spatula to remove, then add more oil to pan.) Slide tortilla from plate into pan, and cook the other side for 15 minutes. Continue to flip, cooking each side 2 additional times for 5 minutes each interval, until center is firm and edges are rounded. Remove to plate and cool to room temperature.

5. To make the aioli, combine 2 yolks, vinegar and  1/4 cup of oil in a food processor. Process until mixture has emulsified, then drizzle remaining oil (1 1/4 cups) in a slow, steady stream. When aioli has thickened, add cooled garlic-sherry mixture, more oil if necessary, and blend until smooth. Check for seasoning and chill.

6. Immediately before serving tortilla, slather a thick layer of aioli over the top, like icing on a cake. Refrigerate leftover aioli for sandwiches or grilled vegetables.

Yield: 12 servings.