Preheat your oven to 375°F (190°C). Line a large baking sheet with parchment paper or lightly coat it with non-stick cooking spray. This prevents the dough from sticking and ensures an easy cleanup later.
Unroll the crescent roll dough and separate it into the pre-cut triangles. Use a knife or a pizza cutter to cut each triangle lengthwise into three smaller, thin triangles. You should end up with 24 small strips of dough in total.
Pat the cocktail sausages dry with a paper towel to remove excess moisture. Place one sausage at the wide end of a dough strip and roll it up toward the point. Place the wrapped sausage on the prepared baking sheet with the point side down to keep it from unrolling.
In a small bowl, whisk together the egg and one tablespoon of water to create an egg wash. Use a pastry brush to lightly coat the top of each dough-wrapped sausage. Immediately sprinkle a generous amount of everything bagel seasoning over the wet egg wash so it sticks well.
Place the baking sheet in the oven and bake for 12 to 15 minutes. The pastry should be puffed up and a beautiful golden brown color. Remove from the oven and let them cool for just a minute or two before serving.