Heat 1 tablespoon olive oil in a non-stick saucepan, add onions and sauté on medium heat for about 15 minutes, stirring often. When soft and well browned, add vinegar and sugar and season lightly with salt and pepper. Cook briefly, and transfer to a bowl to cool.
Split the rolls and toast the two inside surfaces. Butter lightly and set aside.
Grill the bacon, or fry in a hot, non-stick pan with a few teaspoons butter, until crisp. Drain on paper towels. Fry the eggs, sunny side up.
To assemble breakfast sliders place a few spinach leaves on the bottom half of each bun.
Add a slice of cheese cut in half and top with 2 slices of bacon, an egg and a generous spoonful of the caramelized red onions.
Set bun tops in place and serve at once.