Add all of the marinade ingredients to a gallon-sized plastic storage bag. Seal the bag and shake to mix the marinade. Add the mushrooms to the bag, seal, and let marinate while the grill heats up and you make the pesto.

Heat the grill for a few minutes over medium heat.

To make the pesto, add the sun-dried tomatoes and walnuts to a food processor. Pulse a few times until the walnuts and tomatoes are about the size of peas.

Add the cheese, parsley, salt, and pepper to the food processor. Puree for a minute or so while pouring in the olive oil. Puree until the pesto comes together into a thick paste. Set off to the side for later.

Remove the mushrooms from the marinade and add them to the grill. Grill the mushrooms for 6-8 minutes on each side. Turn the mushroom 90 degrees halfway through to get good grill marks on each side.

While the mushrooms are cooking, cut each slice of bread in half. Spread a heaping tablespoon of the pesto on two half slices. Place equal amounts of the shredded cheese on the other two halves. Place each slice of bread on the grill with the topping side up. Grill the bread for about five minutes until lightly golden.

Once the mushrooms are grilled, add them to the pesto slice of bread and top with the cheese topped slice. Serve right away.