1. Pre-heat the oven to 350 degrees.
2. In a small bowl, combine the kosher salt, pepper, and garlic powder. Sprinkle this mixture all over the flank steak, then rub it in gently with your fingers. Let the steak rest for 20 minutes at room temperature.
3. Meanwhile, make the herbed avocado spread. Slice the avocados in half lengthwise and remove the pits. Scoop the flesh into the bowl of a food processer and add the cilantro, basil, and lemon juice. Process until completely smooth, stopping to scrape down the sides of the bowl a few times if necessary. Season with salt and freshly ground pepper to taste. Transfer the spread to a bowl and smooth the top. Press plastic wrap onto the surface of the spread (to prevent browning) and briefly set aside.
4. Heat a lightly oiled grill or grill pan over medium-high heat. When hot, add the steak and cook for 5-6 minutes per side for medium-rare. Transfer the steak to a cutting board and let rest for at least 10 minutes to allow the juices to redistribute. Using a sharp knife, thinly slice the steak across the grain.
5. While the steak is resting, cook the eggs. Add 1 tablespoon of water to each well of a standard muffin tin. One at a time, crack each egg into a ramekin, and then carefully pour it into a prepared well. Transfer the eggs to the oven and cook for 11 minutes until the whites are just set and the yolks are still runny. (There will be a thin layer of water on top of the eggs, which will make it look like the whites are not set, so don’t be fooled!) Let the eggs cool in the muffin tin for 1 minute, then carefully remove them from their wells with a spoon (allow any excess water to drain off) and transfer them to a plate or cutting board.
6. In a bowl toss the arugula with the balsamic vinegar and a pinch of salt and pepper.
7. If you like your rolls toasted, now is the time to toast! I recommend arranging all the rolls (split-side up) on a large baking sheet and popping them under the broiler for 1-2 minutes until lightly toasted.
8. To assemble the sliders: Place a few slices of steak on the bottom half of each roll. Top with an egg, a little bit of arugula, and a couple sliced cherry tomatoes. Spread the top half of the roll very generously with herbed avocado spread and close the sliders. Serve immediately.