Combine the ground beef, dry breadcrumbs, egg, finely chopped onion, salt, and black pepper in a large bowl. Mix with clean hands or a fork only until the ingredients are evenly distributed; overmixing can make the burgers dense.

Divide the mixture into 4–6 equal portions and shape each portion into a patty slightly wider than the hamburger buns. Press the centers gently so the patties cook more evenly and remain relatively flat.

For better flavor and a firmer surface, brown the patties in a skillet over medium-high heat for about 2 minutes per side, working in batches if needed. This optional step takes about 8–10 minutes and creates browned-beef flavor before the slow cooking begins.

Arrange the patties in the slow cooker in a single layer when possible. If your cooker is narrow, stack them carefully with enough room for the gravy to flow around the burgers.

In a bowl, stir together the condensed cream of mushroom soup and the drained sliced mushrooms. Spoon or pour the mixture over the patties, covering as much of the beef as possible.

Cover the slow cooker and cook on LOW for 4–6 hours. Check that the center of the beef reaches at least 160°F internally before serving, since cooking time can vary with patty thickness and slow-cooker models.

Place one Swiss cheese slice on each patty during the last 5–10 minutes of cooking. Keep the lid closed while the cheese melts, since adding it too early can cause it to separate into the gravy.

Toast the hamburger buns if desired, then place a cooked patty on each bottom bun. Spoon some of the mushroom gravy over the burgers, add the bun tops, and serve immediately while the cheese is soft and glossy.