Pat the steaks dry and place on a cutting board. Tenderize the meat well.
Place the steaks into a large bowl. Add the brown sugar, balsamic vinegar, olive oil, parsley, dill, chives, salt, and pepper.
Massage the marinade into the steaks until everything is well blended. Then, cover the bowl with plastic wrap and let it rest in the fridge for at least 1 hour and up to overnight.
Once the steaks have soaked in the marinade, it will be time to cook them. You may choose to cook them closer to when you are ready to assemble the sandwiches. They can be pan fried or grilled. Cook over medium-high heat until cooked to your liking. I prefer medium rare! This is about 5 minutes in a pan over the stove.
Once cooked, slice the steaks into strips against the grain of the meat.
In a large skillet, melt the butter over medium-high heat. Add the mushrooms and cook until they begin to release their own juices, about 5 minutes. Then, add the onion and cook until translucent, another 4 to 5 minutes.
Sprinkle the mushrooms and onions with the sugar, tossing to coat. Deglaze the pan with the white wine and bring everything to a boil, stirring occasionally. Lower the heat to a simmer and cook the vegetables until they are browned and caramelized, about 25 to 30 minutes.
Set these aside while you make the sandwiches.
In a small saucepan, warm the oil. Cook the minced garlic over medium-high heat for about 2 minutes. Set this aside to cool slightly.
In a small bowl, mix together the mayonnaise, sour cream, salt, pepper, parsley, dill, and chives. Stir in the cooked garlic.
If you are not planning to use this right away, place the spread into an airtight container and store in the fridge. It will last for about 5 to 7 days.
Place the broiler in your oven on high. Line a baking sheet with a piece of parchment paper.
Arrange all of the bread on the baking sheet. Divide the strips of steak on one side of each sandwich. Then, layer the provolone cheese over the steak.
Place the baking sheet into the oven for about 2 to 3 minutes or until the cheese is melted. Keep a careful eye on the sandwiches so as not to burn them.
Once the cheese has melted, remove the pan from the oven. Top the cheese with the caramelized mushrooms and onions and arugula. Then, spread the other half of the sandwich with the garlic dill spread. Close the sandwich and serve!
