Slice the onion into thin strips. Rinse the portobello caps to remove any dirt or debris. Use a grapefruit spoon to saw away the protruding stem and remove the gills. Slice each cap in half, then crosswise into 1/4-inch thick strips.

Dry sautee the mushrooms until dry and squeaky, then reduce the heat to medium. Add the butter and then the sliced onions. Sauté the onions over medium heat for a few minutes, or just until they begin to soften. Add a pinch of salt and pepper, the thyme, and oregano.

Once the mushrooms and onions are done, pour in the vegetable broth. Stir to dissolve the browned bits from the bottom of the skillet. Also add the soy sauce, brown sugar, and garlic powder. Allow the liquid to come up to a simmer, then turn down to low and simmer for about 5 minutes while you toast the bread.

Open the rolls and place them on a baking sheet, open sides up. Turn the oven on to broil and place the rolls in the oven. Watch the rolls closely and broil just until you see a slightly browning on the edges (about 5 minutes).

Use a slotted spoon or tongs to take the mushrooms and onions out of the au jus. Divide the mushrooms and onions among the four rolls. Top each sandwich with a slice of provolone. Return the sandwiches to the oven and broil for a few minutes more, or just until the cheese is melted. Close the sandwiches up and serve with the au jus from the skillet for dipping.