For Smoky Aioli Sauce:

Preheat oven to 350 degrees F. Cut tomatoes lengthwise and arrange on shallow pan cut side up. Cut the red onion into 2-inch chunks and add them to the pan along with garlic cloves with skins still on. Drizzle olive oil over the vegetables and sprinkle generously with salt and freshly ground pepper. Add the sprigs of thyme over the top of the vegetables. Cook in the oven for 1 hour or until tomato skins are wrinkled and the vegetables are soft. Let cool. Squeeze the soft garlic out of its skin.

(Variation for roasted vegetables: Fire up the gas grill to high heat and skewer all the vegetables. Drizzle with oil and sprinkle with salt and pepper. Add chopped thyme instead of the sprigs. Grill until soft.)

In a food processor, blend the roasted vegetables, mayonnaise, paprika, cumin, hot pepper sauce and the cooking sherry. Process the mixture until smooth scraping the sides in between pulses. Season with salt and freshly ground pepper to taste. Cover and refrigerate at least 30 minutes or overnight for all the flavors to meld together.

For Potatoes:

Peel and dice the potatoes into 1-inch cubes.

Heat the oil in a large heavy cast iron skillet to a temperature of 300 degrees using a deep fat thermometer. Make sure and maintain this temperature as you cook through the batches of potatoes. You don't want to fry too many at a time as that will crowd them in the pan and bring the temperature down. Also, stir the potatoes as you fry them in order to get them browned nicely on all sides. Stay close and remove in about 5 minutes or so.

Drain potatoes on a plate covered with paper towels. Let them completely cool before continuing the process.

Reheat the oil to 370 degrees. Fry the potatoes again in small batches and remove from oil for 3-5 minutes. Again drain potatoes on a plate with fresh paper towels. Immediately sprinkle with the desired amount of kosher salt.

Drizzle with Smoky Aioli and serve warm. Garnish with chopped Italian parsley.