Preheat the oven to 375 degrees F. Place parchment paper on a baking sheet and then place an 8-inch cake pan in the center to use as a guide for making the wreath.
Cut each sausage in half lengthwise, then cut each half into 3 pieces. Cut the crescent rolls in half from the tip of the triangle to the center of the bottom (see Cook's Note). Roll up each sausage piece in a crescent roll piece. Arrange the rolled sausages around the cake pan flat-side down and touching one another. Remove the cake pan. Egg wash the tops of the rolled sausages to help them stick them together.
Bake the wreath until the dough is golden brown and puffed, 20 to 25 minutes. Let the wreath cool slightly.
Meanwhile, make the Parmesan mustard dip: Mix the sour cream, Parmesan, mustard and chives together in a small bowl until well combined. Season with salt and pepper.
Slowly push the wreath off the parchment and onto a serving platter. Serve with the dip in the center.
You will not need all of the crescent rolls; save for another use.