Preheat the oven to 375°F and line a baking sheet with parchment paper. Cut the crescent roll dough into thin strips and wrap each strip around a sausage, spiraling slightly for that classic look. Place seam-side down on the baking sheet.
Brush each wrapped sausage with the beaten egg, then sprinkle generously with everything bagel seasoning. Bake for 12 to 15 minutes, until puffed and golden brown.
While they bake, stir together the Dijon mustard, maple syrup, and mayonnaise until smooth. Serve warm with the dip on the side.