Mix all of the marinade ingredients together. Cover the mushrooms with marinade on both sides. (For best results, marinate the mushrooms for at least 2 hours.)
IF USING AN OUTDOOR GRILL: Brush grate with oil. Grill the mushrooms for 5-7 minutes on each side. Use the leftover marinade for basting.
IF USING A STOVETOP: Cook mushrooms in a frying pan covered with a tight lid, on medium-low heat, for about 4-5 minutes on each side.
Cooking time may vary depending on the size of the mushroom. If your mushrooms are small, they will need 3 minutes on each side.
While the mushrooms are cooking, toast the buns. You may choose to skip this step.
Spread 1 tsp. of mustard on each bun.
Once the mushrooms are cooked, lift the lid, place the cheese on top, and return the lid, allowing the cheese to melt.
Transfer the mushrooms to the buns, top with fried onions, and assemble the burger.