In a large skillet, sauté mushroom sand onion in butter until tender; set aside.
In a large bowl, combine the egg, milk, oats, salt and pepper. Crumble beef over mixture and mix well.
On a large piece of heavy-duty foil, pat beef mixture into a 12 x 8 inch rectangle; spoon mushroom mixture to within 1 inch of edges. Roll up jelly-roll style, starting with a short side and peeling foil away while rolling. Seal seam and ends. Discard the foil.
Prepare grill for indirect heat, using a drip pan. Form a double thickness of heavy-duty foil. Place meat loaf on foil; place on the grill rack over drip pan.
Grill, covered, over indirect medium heat for 35 minutes. Combine sauce ingredients; brush over loaf. Grill 15-20 minutes longer or until meat is no longer pink and a meat thermometer reads 160°F Let stand 15 minutes before slicing.