Pot roast and au jus: create a quick spice blend by adding salt, black pepper, and garlic powder to a small bowl. This is your meat seasoning blend.
Cut the chuck roast into 2 to 3-inch square pieces. Coat each piece in Dijon mustard and then sprinkle the spice blend on all sides of each piece of meat. If you don't end up using all the seasoning, you can reserve it for seasoning pretty much anything.
Add a tablespoon of oil to a large pan over medium-high heat. Once the oil starts shimmering, add half of the beef pieces and cook for 4 minutes per side. Flip each piece over and cook for another 4 minutes on the second side. Remove the meat and place it into a slow cooker while you cook the onions, garlic, and braising liquid.
Reduce the heat under the pan to medium.
Add the sliced onions to the pan where the beef was and cook for 6 minutes. After 6 minutes, add minced garlic and cook for another 1 to 2 minutes, stirring often.
Once the garlic has cooked for a couple of minutes, add red wine, beef broth, Dijon mustard, brown sugar, and salt, and stir to combine everything.
Bring the mixture to a simmer, turn off the heat, and pour all of the braising liquid into the slow cooker with the beef and cook on high for 3.5 hours or low for 7 to 8 hours.
After the time has elapsed, with a slotted spoon, remove all beef pieces to a cutting board, leaving the liquid still in the slow cooker. Break each piece of beef apart with two forks to break it into smaller pieces.
Keep the beef in its own container and package the au jus or broth in a separate container. Store both in the fridge until it is time to make the sandwiches.
Horseradish mayonnaise: combine mayonnaise and prepared horseradish in a small bowl. Stir to incorporate well.
Warm the meat and au jus: you can warm the meat in the microwave, in a skillet for 5 minutes over medium heat, or in a pot along with the au jus. If you're heating up the meat in a skillet, you can microwave the au jus for a minute or so, or you can warm it up in a small pot until it's just starting to simmer.
Sandwich assembly: preheat the oven to 350°F or turn on the broiler.
Add a generous spread of horseradish mayonnaise on the bottom of a six-inch sub-style roll. Top with a pile of warmed beef and cover that with 1 to 2 slices of cheddar cheese, broken up so it fully covers the meat. Broil the bottom bread covered with meat and cheese, and the dry inside top of the bread until the cheese is melted. If you're using a 350°F oven, cook the open-faced sandwich for 5 to 7 minutes or until everything is warmed and the cheese is melted.
Remove the sandwich from the oven and add red pepper relish on top of the melted cheese. Spread a bit more horseradish mayonnaise on the top roll and close the sandwich to finish.
Serve with a small portion of au jus for dipping and enjoy.
Notes:
No slow cooker? If you do not have a slow cooker, you can cook this same recipe in an oven-safe pot or roasting dish with the lid on. You can set your oven to 375°F (190°C) and cook it for around 3.5 hours. The oven does allow more moisture to evaporate than a slow cooker, so you may want to add just a little bit more beef broth (around 1/2 cup) and check it at the halfway point to see if it’s losing a lot of liquid. You just want to make sure that the beef is mostly covered by the braising liquid.