Cook your sausage links according to package directions until they're fully cooked and nicely browned. Set aside on paper towels to absorb excess grease. (If you're in a rush, you can use pre-cooked sausage links, just warm them up slightly.)
Flatten each bread slice with a rolling pin or the flat side of a knife. Don't go nuclear – you just want to compress them enough so they'll roll without breaking.
Whisk together the eggs, milk, sugar, vanilla, cinnamon, and salt in a shallow bowl wide enough to dip your bread. Make sure everything is well combined – nobody wants a surprise pocket of cinnamon.
Place a sausage link at one end of each flattened bread slice and roll it up tightly, pressing the seam to seal. If it's being stubborn, you can secure it with a toothpick, but usually the next step takes care of that.
Dip each roll-up in the egg mixture, making sure to coat all sides. Don't let it soak too long or you'll have a soggy situation on your hands.
Melt a tablespoon of butter in a large skillet or on a griddle over medium heat. Working in batches (about 4 at a time), place the roll-ups in the pan with the seam side down first to seal them.
Cook for about 2-3 minutes per side, turning occasionally, until all sides are golden brown and crispy. Add more butter to the pan between batches as needed.
Transfer to a plate and either serve immediately or keep warm in a 200°F oven while you finish cooking the rest.
Serve with maple syrup for dipping or drizzling, and add any optional toppings you like.