Preheat the oven to 400ºF.
Crack the eggs into a bowl or liquid measuring cup and whisk with the milk and salt until even in colour. Ladle out about 1/3 cup of the eggs into a small bowl and save this for brushing on the pastries.
Melt the butter in a non-stick pan over low to medium low heat, and pour in the eggs. The eggs should begin solidifying quickly on the bottom of the pan.
Use a silicone spatula to scrape the solidified egg gently from the edges of the pan toward the center. Keep repeating this process until most of the egg has solidified and rumpled up and resembles soft set scrambled eggs.
Sprinkle the cheese over the top and continue pulling the spatula from the edge toward the center of the pan until the cheese is melted and no liquid egg remains. Stir in the thinly sliced green onions.Remove the pan from the heat and spread the eggs on a large plate and transfer to the refrigerator to cool, stirring from time to time.
Unfold 1 sheet of puff and cut straight down along the fold lines (lengthwise) to create 3 long rectangles. Then cut across them in the center to create 6 evenly sized rectangles.
Separate the rectangles and place them on the parchment paper, leaving at least 2 inches between each rectangle. Set the pan in the refrigerator.
Lightly flour your work surface and unfold the second sheet of puff pastry. Roll it gently with a rolling pin until it is about 4 inches wider and 4 inches longer than it was, or 14" by 19". Once again, cut this along the fold lines (they should still be barely visible) lengthwise into 3 long rectangles, then crosswise once down the center so you have 6 slightly larger rectangles than you got from the first sheet.
Take the pan of puff pastry rectangles from the refrigerator. These will be your bases.
Brush the perimeter of the bases lightly with the reserved egg wash. You do not need to brush the whole pastry base.
Divide the cheesy scrambled eggs evenly between the bases, leaving a 1-inch perimeter, using your hands to mound the eggs slightly. Nestle 2 fully cooked breakfast sausage links lengthwise in the center of the eggs.
Lay one larger pastry rectangle over each topped base. Tuck any filling that's falling out back under the pastry.
Use a fork to crimp the edges gently together. Don't mash them mercilessly, but use enough pressure to leave fork marks and press the pastry together.
Use the remaining egg wash to brush the tops of the pastries. Use a sharp knife to cut to small vent slashes in the top of each pastry.
Bake for 25 to 30 minutes, or until the pastry is puffed and set and is a deep golden brown. Remove the pan from the oven and let the pastries rest on the pan for 5 minutes before serving.