Combine the mushrooms, oil, and Essence in a medium bowl and toss to coat evenly.
Prepare a stovetop smoker according to the manufacturer's instructions. Place the mushrooms on the grill pan and cover the smoker, leaving the lid ajar by 1-inch. Place over medium heat on top of the stove. When it begins to smoke, close the lid completely. Cook until the mushrooms are tender and completely smoked, about 20 minutes. Remove from the smoker and set aside until ready to assemble the quesadillas.