Preheat your smoker to 275 degrees Fahrenheit. I would recommend a nice fruit wood as your smoking flavor.
Clean the mushrooms and remove the stems. Make sure to set the stems aside. Remove the very bottom of the stem and then dice the remaining mushroom up into small pieces.
In a large bowl, combine the mushroom stems, bread crumbs, parmigiana cheese, minced garlic, chopped parsley, salt and pepper and 3 tablespoons of olive oil. Depending on the size of the stems you may need more olive oil. You want the mixture to be moist but not soaking.
Arrange the mushrooms in a disposable pan and then use a spoon to fill the mushrooms. Fill the mushrooms until they are heaping and then drizzle with a little more olive oil. You may have extra filling depending on the size of the mushroom cavities.
Place the pan in the smoker and cook for 1 hour and 20 minutes or until the mushrooms are tender and the filling starts to brown.
Remove from the smoker and serve.