Whisk or stir the condensed brown sauce in a medium bowl until smooth. (If it is very thick, you can simply add a little water to thin it out, but not so much that it ends up being a thick sauce.)
Pour the sauce evenly over the beef rolls, making sure each roll is well coated and there is sauce in the bottom of the pan. Use a spoon to press the sauce in between the rolls if necessary.
Cover the baking dish tightly with foil to keep the rolls moist. Bake in the preheated oven for 45 to 60 minutes, or until the meat is tender when pierced with a fork and the cheese inside has melted.
Carefully remove the foil, then bake uncovered for another 5 to 10 minutes to thicken and give the sauce a slightly darker color on top.
Let the beef rolls rest for about 5 minutes before serving. Spread extra sauce from the bottom of the pan over each portion, making sure everyone gets some of the mushrooms and melted Swiss cheese.
Variations and Tips
If you're picky, you can skip the mushrooms in some of the rolls and just fill them with Swiss cheese, then mark them with a toothpick so you know which is which. For a milder flavor, you can use baby Swiss cheese or even provolone cheese instead of regular Swiss cheese. If your steak slices are very thin and delicate, you can secure the rolls with toothpicks before baking; just remember to remove them before serving. To stretch the meal for a larger family, you can cut the finished rolls into medallions and spread them over mashed potatoes or noodles, then spread the sauce on top. For a slightly lighter version, you can use a can of sauce and serve the rolls over buttered noodles, so that the noodles help soak up the extra juices. You can also make it ahead of time: Assemble the rolls and pour the sauce over them, cover and refrigerate for up to 24 hours, then bake a little longer straight from the refrigerator until everything is warm and tender.
