Begin by flattening each slice of bread with a rolling pin and trimming off the crusts.

Position a sausage link at one edge of a flattened bread slice and tightly roll it up. Repeat the process with the remaining bread slices and sausage links.

In a bowl, thoroughly whisk together the eggs, milk, cinnamon, and vanilla extract.

Coat each roll-up in the egg mixture, ensuring they are fully submerged.

Preheat a skillet with butter over medium heat. Fry the roll-ups until they achieve a golden-brown color all over.