Arrange a rack in the middle of the oven and heat the oven to 375°F. Line a rimmed baking sheet with parchment paper.

Pat 16 breakfast sausage links dry with paper towels. Unroll 1 can refrigerated crescent roll dough on a work surface. Separate the dough along the perforated seams into 8 triangles. Use a pizza cutter or sharp knife to cut each triangle lengthwise into 2 narrow triangles, 16 total.

Place 1 large egg and 1 teaspoon water in a small bowl and whisk with a fork until combined.

Brush the dough with a thin layer of the maple syrup, about 2 1/2 teaspoons.

For each pigs in a blanket, place 1 sausage at the wide end of a dough triangle. Roll towards the pointed end, wrapping the dough around the sausage and allowing the dough to overlap.

Place the pigs on the blanket on the baking sheet seam-side down, spacing them evenly apart.

For everything bagel pigs in a blanket, brush the tops and sides with a thin layer of the egg wash, then sprinkle with 1 tablespoon everything bagel spice. For maple syrup pigs in a blanket, brush the tops and the sides with the remaining 2 1/2 teaspoons maple syrup.

Bake until the dough is puffed and golden brown, 13 to 15 minutes. Serve warm with more maple syrup for dipping the sweet-savory pigs in a blanket if desired.