Preheat the oven to 350°F. Spray a 9x13-inch baking dish with nonstick cooking spray and set aside.
In a large skillet over medium heat, melt 4 tablespoons salted butter. Add 3 cups small-diced onion, 2 teaspoons granulated sugar and ½ teaspoon black pepper to the skillet and stir to combine. Continue to cooking, frequently stirring, until the onions turn a golden brown color. Take off the heat and place it on a separate plate until ready to assemble the squares.
Unroll one of the 2 tubes crescent dough sheets and press it into the prepared baking dish. Make sure it goes up the sides of the dish about 1 inch.
Lay half of the 8 ounces sliced provolone cheese on top of the dough.
Layer 14 ounces deli sliced roast beef on top of the cheese.
Spread out the cooked onions on top of the roast beef.
Place the remaining provolone cheese on top.
Unroll the second crescent dough sheet and place it on top. As good as you can, pinch the two doughs together along the seams to form a pocket, and tuck the excess dough under the bottom.
Whisk together 1 large egg, 1 ½ tablespoons dried onion soup mix, 1 teaspoon dried parsley flakes, and ½ teaspoon dried thyme in a medium-sized bowl.
Brush the egg mixture all over the top of the dough, and use it all.
Cover with nonstick foil and bake for 30 minutes. Take the foil off and bake an additional 15-20 minutes until deep golden brown on top.
Let cool for 10 minutes.
While the squares are cooling, make the 1 ounce packet au jus gravy mix per the directions on the back of the package (using the 3 cups cold water).
Cut into squares and serve with au jus for dipping.
Notes
If you don't enjoy onions, just skip that step.
Allow these to cool a bit before slicing. They slice much easier when they aren't so hot straight out of the oven.
When you first cut into them, some juice will release from the inside, that’s normal. If you don't like extra juices, just soak it up with a paper towel.
Other cheese that would be good, white cheddar, mozzarella, gruyere, swiss, or gouda.
Keep leftovers in the fridge for up to 3 days. Freeze for up to 3 months.
I suggest reheating leftovers in the oven until warmed through. You could even use an air fryer. Microwaving them may make them soggy. Keep an eye on them, you may need to cover with foil if the top begins to brown more.