Heat your Blackstone to medium heat and add a bit of olive oil. Toast one side of the sourdough bread slices.
In a food processor, combine flat-leaf parsley, cilantro, lime juice, garlic cloves, red pepper flakes, ¼ cup of olive oil, and a pinch of salt and pepper. Blend until smooth to create the chimichurri sauce.
In a small bowl, mix mayonnaise with some of the chimichurri sauce to evenly incorporate the flavors.
Add a bit more oil to the griddle and crack the eggs. Cook the eggs to your desired doneness, seasoning with a pinch of salt and pepper.
To assemble the sandwich, spread a generous amount of the chimi-mayo onto the toasted side of each bread slice.
Layer arugula on top of the mayo, followed by 2 slices of prosciutto. Add tomato slices seasoned with salt and pepper, and then arrange avocado slices. Place the cooked egg on top and garnish with a light drizzle of chimichurri sauce.
