Step 1

Carmelize onions. Melt 2 tablespoons f the butter in a large skillet set over high heat. When it foams, add the onions and sprinkle with salt. Do not stir immediately. Wait 1 minute, then begin to stir frequently over high heat for 5 minutes or so, or until the onions have released some liquid and started to become translucent.

Step 2

Reduce the heat to medium, and cook, stirring often, for what will seem like a very long time, until the onions are fully melted and dark golden brown, approximately 30 minutes. Remove onions, and set them and the skillet aside.

Step 3

Take a small baking dish, and put into it olive oil, soy sauce, balsamic vinegar and minced of garlic. Add portobello caps, then cover with foil, and roast in a 400-degree oven for 30-45 minutes, turning once.

Step 4

Set the skillet to medium heat, and put four pieces of rye bread into the butter that remains from cooking the onions. Top each piece with a slice of cheese, then two portobello caps, then some of the caramelized onions, and finally another slice of cheese and another slice of tye. Use the spatula to press down on the packages, and after about a minute or so, carefully turn over each patty to begin to brown the other side. Cook until the cheese is fully melted and the bread is golden brown and crisp on both sides. Slice in half before serving.