Heat the olive oil in a skillet over medium heat. Add the mushrooms and 1/4 teaspoon of the salt. Cook, stirring occasionally, until the mushrooms have released their moisture and are lightly browned. Set aside to cool.

In a large bowl, combine the ground beef, egg, breadcrumbs, milk, Worcestershire sauce, black pepper, and the remaining 1/4 teaspoon of salt. Mix gently until just combined.

Stir the softened cream cheese and shredded Swiss together in a small bowl. On a sheet of parchment, shape about two-thirds of the beef mixture into a rectangle. Spread the cream cheese mixture down the center, then spoon the cooled mushrooms over it. Leave a border around the edges.

Shape the remaining beef mixture over the filling. Pinch the edges and ends together to seal, then form the loaf into an even shape. Transfer it to a smoker-safe pan.

Heat the smoker to 250°F and add the wood chips according to the smoker’s instructions. Place the meatloaf 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. Rest the meatloaf for 10 minutes before slicing.

While the meatloaf rests, whisk 1/2 cup of beef broth with the flour until smooth. In a small saucepan, bring the remaining 1 cup of beef broth and dried thyme to a gentle simmer. Whisk in the flour mixture and cook, stirring, until the gravy thickens. Stir in the chopped parsley.

Slice the meatloaf carefully so the filling stays in place. Serve with the herb gravy spooned over each portion.