Remove the spam from the can. You only need 2 slices, so cut out 2 (¼-inch) large slices (6 slices in 1 can). Transfer the rest of the spam to an airtight container and chill in the fridge for other uses.
In a small bowl, combine mayo and chili sauce. Set aside.
In a large skillet over medium heat, melt ½ tablespoon butter. Place the buns cut side down and toast for a couple minutes, until nicely toasted. Turn them over and toast for another 30 seconds. Transfer the buns to a working surface. Wipe the skillet clean with a paper towel.
In the same skillet over medium heat, place 2 slices of spam. Cook until nicely brown on both sides, about 4 – 6 minutes total. Transfer to a plate lined with a paper towel.
In the meantime, in a medium skillet over medium heat, heat until hot. Melt ½ tablespoon butter. Add the eggs. When the outer edges turn white in color, cover with a lid. Turn down the heat to low and cook for 3 more minutes. Transfer to a plate.
To assemble, spread a good amount of mayo on each bun. Place a handful of baby arugula over the bottom buns. Add spam, then fried egg. Last top with top buns. Serve immediately.