Preheat oven to 400°F (200°C).
Crack eggs into a bowl and whisk for 30 seconds. Add hot sauce and a pinch of salt, then whisk again.
Melt ½ tablespoon butter in a nonstick pan over medium-low heat. Add eggs and cook slowly, stirring continuously until soft curds form.
Add most of the cheese (reserve a small portion) and continue cooking until a semi-firm cheesy egg mixture forms. Transfer to a bowl.
In the same pan, melt remaining butter. Add sliced onions and a pinch of salt. Cook over medium heat for 10 minutes, stirring often.
Stir in balsamic reduction and cook for 1 more minute. Add cooked beef sausage and heat through. Set aside.
Lightly flour a surface and roll out one sheet of puff pastry. Cut into 6 rectangles and place on a lined baking tray.
Evenly divide the cheesy eggs and sausage-onion mixture among the rectangles.
Brush edges with egg white.
Roll out the second pastry sheet and cut into 6 rectangles. Place on top and seal edges with a fork.
Cut two small slits on each pastry to release steam.
Brush tops with egg white, sprinkle everything seasoning, and add remaining cheese.
Bake Savory Breakfast Pop Tarts with Cheesy Eggs for 20 minutes, rotating the tray halfway, until golden brown and crisp.