Form the sausage into several small patties, then place oil in a sauté pan over high heat. When the oil is smoking, add the sausage and leave it until it gets a nice sear on one side, then flip. Once browned on each side, use a wooden spoon to break it up into smaller pieces. Once cooked through, set aside on a place and allow to cool to room temperature.
While the sausage cools, divide your puff pastry into three rectangles (many puff pastries come in three strips with perforations indicating thirds). Take one rectangle, lightly flour both sides, then using a rolling pin, roll it to at least 5 inches wide, but not so thin that it becomes translucent. Divide your rolled-out rectangle in half, then trim each half into a square. Discard the trimmed edges. Repeat with the remaining two sheets so that you have 12 squares. Set aside.
In a medium bowl, mix together the sausage with the cream cheese. Take one square of puff pastry, and line roughly 1 tablespoon filling diagonally across the top, from one corner to another. You may need more or less filling depending on the size of your pastry square. Sprinkle the filling with a large pinch of cheddar. Fold the top corner over the diagonal of filling and press into the bottom corner to make a triangle-shaped pocket. Press the edges down to seal it, then fold the point of the triangle over the base, then bend the ends of the triangle back around to meet each other. Brush with egg wash and set on a baking sheet. Repeat for the remaining 11 squares. Depending on the size of your squares and the amount of filling you use in each, you may not use the entire mixture up—if not, discard or freeze the remainder for next time!
Note: If your crescents look wrinkly and sad when raw, don't worry—they'll puff up and look nicer as they bake!
Bake at 375° F for 15 minutes, until golden brown. Serve fresh out of the oven.