Preheat a smoker to 250°F. Use your preferred mild smoking wood and set out a loaf pan or rimmed tray for shaping the meatloaf.
Heat a skillet over medium heat. Add the chopped mushrooms and cook for 5 to 7 minutes, stirring often, until they release their moisture and become tender. Let them cool.
In a small bowl, mix the softened cream cheese, shredded Swiss, parsley, garlic, and dried thyme until evenly combined.
In a large bowl, combine the ground beef, egg, breadcrumbs, cooled mushrooms, Worcestershire sauce, salt, and black pepper. Mix gently until just combined.
On a sheet of parchment, shape about two-thirds of the meat mixture into a rectangle. Spread the cheese mixture down the center, leaving a border around the edges. Shape the remaining meat mixture over the filling, then pinch the edges together to seal. Form it into a compact loaf.
Place the loaf in the smoker and cook until the center reaches 160°F on an instant-read thermometer, about 2 to 3 hours depending on its shape and the smoker. Brush the barbecue sauce over the top during the final 20 minutes.
Transfer the meatloaf to a cutting board and let it rest for 10 minutes before slicing. This helps the cheese filling settle and keeps the slices intact.