Preheat the oven to 375ºF and line a rimmed baking sheet with parchment paper.
Pat the breakfast sausage links dry with paper towels to remove excess moisture.
Unroll the crescent roll dough and separate it into eight triangles along the perforated seams.
Cut each triangle in half lengthwise using a pizza cutter or sharp knife to create 16 narrow triangles.
If using the everything bagel option, whisk an egg with water in a small bowl.
If using the maple syrup option, brush each dough triangle with a thin layer of maple syrup.
Place one sausage link at the wide end of each dough triangle and roll it towards the pointed end, wrapping the dough around the sausage.
Arrange the rolled pigs in a blanket seam-side down on the prepared baking sheet, spacing them evenly apart.
For the everything bagel version, brush the tops and sides with egg wash and sprinkle with everything bagel seasoning.
For the maple syrup version, brush the tops and sides with additional maple syrup.
Bake for 13 to 15 minutes until the dough is puffed and golden brown.
Serve warm, with extra maple syrup for dipping if desired.