Step 1

Place racks in upper and lower thirds of oven; preheat to 375°. Unroll one 8-oz. can refrigerated crescent rolls onto a cutting board and tear sheets at perforations to separate into triangles. Cut each triangle lengthwise into 3 thin equal-size smaller triangles. Tidy up edges to make even if desired.

Step 2

Working one at a time, place sausages from one 10-oz. package smoked cocktail sausages or franks on the short ends of triangles of dough; roll up and gently press point end to seal. Divide between 2 parchment-lined baking sheets, placing point side down (you should have 24 total). Brush dough with 1 large egg, beaten to blend. Bake until dough is cooked through and golden brown, 13–15 minutes.

Step 3

Transfer pigs in a blanket to a platter and serve with Dijon mustard for dipping.