Preheat oven to 400 degrees F. In a mortar and pestle or a small bowl, mix together the salt, pepper, dried oregano and thyme and red pepper flakes. Rub the mixture all over the beef round. Pour a teaspoon of olive oil in the bottom of a cast iron skillet or roasting pan and place the beef round inside. Transfer to the oven to roast for 20 to 25 minutes, until the internal temperature reads 125 degrees F for medium-rare. Transfer to a wire rack and allow to rest for about 10 minutes before slicing. Just a note: if you’d like it medium, cook it in the oven until the internal temp reads 140 degrees F, about 35 minutes.
To make the au jus (you can do this while the beef is in the oven), add a teaspoon of olive oil to a medium pot that’s set over medium heat. When the oil is hot, add the onions and pinch of salt; cook until fragrant and slightly softened, about 2 to 3 minutes. Mix in the garlic clove, dried thyme, pepper, worcestershire, dry sherry and beef broth; give it a good stir and bring the mixture to a simmer. Once it reaches a simmer, turn the heat down to medium-low and allow to continue simmering for about 20 minutes, until the au jus is reduced by about half. Cover the pot and keep the heat on very low until you’re ready to assemble the sandwiches.
In a small bowl, mix together the prepared horseradish and mayonnaise until nearly smooth. Give it a taste and adjust the horseradish according to your liking.
To assemble the sandwiches, start by slicing up the beef round. Take a very sharp knife (I had luck with a serrated knife), slice the beef as thinly as possible. I found that scraggily slices were the best texture—don’t worry if they’re not perfect, beautiful slices! Swipe the inside of your hoagie bread with a bit of horseradish mayo; dip the slices of beef into the au jus and place them in the hoagie. Top with a few slices of provolone cheese. If you’re feeling crazy, transfer the sandwiches to the oven so the provolone gets all melty. Serve sandwiches with a side of au jus.