1) Preheat oven to 350 degrees F. Bake bacon on a baking sheet for 15-20 minutes until very crispy. Toast rolls.
2) For glaze, add balsamic vinegar and sugar to a small pot over low heat. Heat, stirring constantly, until mixture simmers. Keep heat low and stir for 6-8 minutes until mixture thickens. It should coat the back of a spoon. Remove from heat and let cool.
3) Fry eggs in a little butter or oil until they are cooked to your liking. I recommend leaving the yolks soft. If you want to do them sunny-side up, fry them for about 2 minutes until the whites are cooked, then cover them with a plate or lid for 30 seconds to set the top of the egg.
To make a sandwich, slather a little mayo on the bottom of a roll. Add a handful of arugula and sliced strawberries. Top with crispy bacon, cooked egg, and drizzle with glaze.