For the prime rib rub: Preheat oven to 450 degrees F.
Mix the garlic, salt, pepper, granulated onion, thyme and rosemary together in a small bowl. Pour the Irish stout and 2 cups water into a large metal roasting pan fitted with a rack inside. Rub seasoning mix all over prime rib and place in the roasting pan fat-side up. Roast, uncovered, 30 minutes. Reduce oven temperature to 325 degrees F. Cover roast with tin foil and roast until a meat thermometer inserted into the thickest part registers 145 degrees F for medium-rare, about 2 hours. Transfer to a cutting board, wrap in foil and let rest for 20 minutes before slicing. Save drippings in pan to make au jus.
For the horseradish aioli: Place yolks, garlic, horseradish, lemon juice, Dijon and salt into a food processor. Process until smooth, then drizzle in olive oil until it reaches desired consistency.
To make au jus, pour pan drippings into a small saucepan. Add black pepper and minced garlic to taste. Add water if more au jus is desired than what was left from roasting the meat. Bring to a simmer on stovetop, and simmer a few minutes.
To make the sandwich: Soak a 1/3-pound slice prime rib in au jus briefly, then saute in a pan to warm, and top with two slices of white Cheddar. Served on a demi-baguette with 2 ounces of horseradish aioli, along with a side of au jus for dipping. Repeat with 5 more slices.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.