Roast beef and gravy: preheat your oven to 275 F (135 C).

Liberally salt the exterior of the chuck roast and allow it to sit on a cutting board for 30 minutes. After the beef has rested, dry off the exterior with paper towels to ensure it is dry. The salt will bring moisture to the surface and if the surface of the meat is damp it will not sear properly in the next step. So, dry it off.

On your stove, over high heat place a large pot or Dutch oven. Add 3 tablespoons of oil and allow it to heat up until the oil is shimmering. Once the oil is shimmering, add the roast and sear it on each side for 7 minutes. Once at least 3 sides have been seared remove the roast to a plate to rest for the next step.

Remove the pot from the heat and allow it to cool for 5 minutes while you chop your onions. After 5 minutes, add the pot back to medium heat and add 3 tablespoons of butter.

Once the butter is melted and bubbly add onions and cook for 4 or 5 minutes to soften them.

Add the minced garlic and cook for around 1 minute, stirring everything together.

After 1 minute, add 3 tablespoons of all-purpose flour, stir, and cook for another 1 minute to cook off the flour taste.

Pour 1 tablespoon of Worcestershire sauce, and 1 tablespoon of beef bouillon base into the onions. Stir everything well to combine and as soon as it's all combined you can add 3 cups of beef stock.

Bring everything to a simmer and then add the chuck roast back into the pot. Taste the gravy for seasoning. If it doesn't seem salty enough, add 1 or 2 teaspoons of salt.

Place the lid on to cover the beef and gravy and place in the oven to bake for 4 hours. 

After 4 hours remove the pot from the oven and remove the lid from the pot. Allow the beef to rest in the gravy for 30 minutes. Once 30 minutes have passed, remove the beef to a sealed container or wrap it in plastic and foil and place it in the refrigerator to cool. It's easier to slice when it is cool.

Place the gravy in another sealed container to be used later when it's time for sandwiching.

After about 2 hours you can slice the meat into 1/4 inch or thinner slices. Or you can wait until it's time for sandwiches to slice.

Prepare the giardiniera: place 1/4 to 1/2 cup of giardiniera on a cutting board. With a paper towel, dry off some of the excess oil from the giardiniera, trying to remove as much as possible because extra oil might make your cheese not set properly. After the pickled veggies are dry, chop them into very fine pieces.  

Giardiniera cheddar cheese slices: add a greased or Silpat lined sheet pan to your oven on its lowest setting. Mine is 150 F.

Add water to a medium-sized pot and bring to a simmer. Add sodium citrate and stir to combine.

Slowly add all the shredded cheese, stopping to stir the cheese into the sauce after every handful. Once all the cheese is added stir very well while the cheese is still simmering to make sure it is very smooth.

Add the finely chopped giardiniera and stir again to incorporate it thoroughly into the cheese sauce.

Once the giardiniera is fully mixed in, carefully pour the sauce over the warm sheet pan and shake the sheet pan to allow the sauce to spread out. You may need a knife or offset spatula for this. Once the sauce is in a consistently thin layer, cover the cheese with wax paper and move it to a refrigerator to cool.

Once the cheese is fully cool, you can carefully remove it from the sheet pan and slice the cheese into 3.5-inch squares or whatever shapes you desire. To store the cheese, place a piece of parchment or wax paper between each slice and store it in the refrigerator for up to three weeks.

Sandwich assembly: in a small pot add beef and a couple of large spoonfuls of gravy. Cook over medium heat for about 5 minutes or until the meat and gravy are warmed all the way through.

Add the beef and a bit of gravy to the middle of a split sub roll and top with a slice or two of giardiniera cheese. 

Add the sandwich to a broiler and broil for 4 to 5 minutes or until the cheese is melty and the bread is starting to brown a little. 

Add more giardiniera if desired. Serve and enjoy.