Place the Neufchatel in a medium mixing bowl. Set aside to come to room temperature. Heat the oven to 400°F. Line a baking sheet with a nonstick silicone baking mat or parchment paper. Set aside. Unroll the puff pastry and place the parchment paper that comes with the pastry on top of the prepared sheet pan. Place in the refrigerator while you prepare the filling
Heat a large skillet over medium-high heat. Add the breakfast sausage and cook, using a spatula to break up the meat into smaller pieces. Once the meat is no longer pink, about 3 minutes, add the grated onion and apple. Stir to combine. Reduce the heat to medium low and cook until the mixture is dry and the onions are soft and translucent about 3 minutes. Set aside to cool slightly.
Transfer the sausage mixture to the bowl with the cheese. Add the herbs and season with pepper. Using a spatula or handheld mixer, stir to combine.
Remove the puff pastry from the refrigerator. Remove the parchment and puff pastry from the sheet pan. Spread the sausage mixture across the entire dough. Sprinkle with smoked paprika, cayenne pepper, and freshly ground pepper. (The cheese is salty, so there’s no real need for additional salt.)
Starting from the long end, roll the puff pastry into a log. Tightly wrap the log in the parchment. Place in the refrigerator for 20 minutes. (You don’t have to use the sheet pan.)
You can use a sharp knife, but the best way to achieve circular pinwheels is to use unflavored dental floss. Wrap a length of dental floss around the log where you want to cut, then gently pull the ends in opposite directions to slice cleanly through the log. Cut the log in half. Return one-half to the refrigerator. Working with the remaining half and dental floss, cut the log into 15 pieces about 1/3 inch thick. Place the pinwheels on the silpat-lined baking sheet.
Transfer to the heated oven and cook until dark golden brown, about 18 minutes. Remove to a rack to cool slightly. Repeat with the reserved chilled roll.
Store in an airtight container in the refrigerator for up to 3 days. Serve room temperature with mustard for serving.