In a small bowl, mix the satay sauce and peanut butter together. Set aside.
In another small bowl, combine sugar, soy sauce, sesame oil, water and white pepper. Set aside.
In a large nonstick skillet over medium-high heat, add 1 tablespoon vegetable oil. Add beef and saute until no longer pink. Transfer the beef (with juice) to a medium bowl. Wipe the skillet clean with paper towels.
In the same large skillet over medium-high heat, add ½ tablespoon oil. Add garlic and cook for 1 minute. Add the satay and peanut butter mixture. Stir and cook for 1 minute. Pour in the soy sauce mixture. Bring to a boil and cook for 2 minutes. Put the beef back and cook for 2 more minutes. Transfer to a medium bowl.
Place bread in toaster to toast lightly. Spread a layer of salted butter on each toast.
In medium non-stick skillet over medium heat, melt 1 tablespoon unsalted butter. Season the beaten eggs with salt. Once the butter is bubbling, add eggs. When the eggs start to set, run a spatula through the middle of the eggs to create soft curds. Repeat until the eggs are just cooked through. Transfer to a medium bowl.
To assemble, place 2 slices of toast on a chopping board. Divide the egg mixture and put on top of the toast. Top with satay beef. Cover each sandwich with another slice of bread. Cut the sandwiches in half. Serve immediately.