For the jam:

Heat olive oil in a nonstick skillet. Once hot, add the cherry tomatoes and garlic. Season with salt and pepper.

Cook the tomatoes and garlic for a few minutes, stirring occasionally. As the tomatoes begin to soften, press them down gently with a potato masher. Once they start to break apart and release their juices, add the honey, dried basil, and balsamic vinegar. Continue to cook down until syrupy and thickened, about 10 minutes.

For the sandwich:

Preheat oven to 400 degrees F.

Cut ciabatta rolls in half and lightly brush cut sides with olive oil. Place rolls on a sheet pan and toast in the oven for 8–10 minutes.

In a skillet, heat 1 teaspoon olive oil over medium heat. Add slices of prosciutto. Cook slices for 1 minute on each side.

Using the same pan, fry the eggs.

To assemble the sandwiches, place arugula on the bottom of each roll. Next, add the crispy prosciutto followed by the fried eggs. Spread tomato jam on the other half of the rolls and place on top of eggs. Serve immediately.