Light your grill and set up for two zone cooking, establishing the temperature at 350°F. Add one chunk of pecan (or wood of choice) to the hot coals.
While the grill is preheating, in a large stockpot bring six cups of water to a boil over high heat. Add quarter cup kosher salt to the water, along with the trimmed green beans. Boil the beans for five minutes before removing and shocking them in an ice-water bath to prevent them from cooking further.
While the beans cool, place a large saute pan over medium-high heat and add the olive oil. When the oil is hot, add the mushrooms and spread them out evenly. Don’t over stir them, just let them brown on both sides and allow the water from the mushrooms to evaporate. About five minutes.
Add the butter and let it to melt, mixing it in with the mushrooms to ensure even coating. Remove the mushrooms from the heat and set aside.
Remove the beans from the ice bath, and dry them with a paper towel. Place them in a large mixing bowl and add the soup, mushrooms, two teaspoons salt, cayenne, white pepper, garlic, half of a cup of parmesan cheese and one cup of the fried onions. Gently fold those ingredients together and transfer to a cast-iron skillet or oven-safe vessel. Then, top with remaining cheese, fried onions and smoked paprika.
Place the casserole on the grill over indirect heat, and close the lid. Allow it to smoke roast for 35 - 40 minutes. Remove from the grill and serve hot.