Place the chicken breasts in between two large pieces of plastic wrap, and using a mallet pound them out until it is about 1/4" to 1/2" thick.
In a medium-sized baking pan or shallow bowl, mix together the flour, salt, and pepper and set aside.
In a separate second medium-sized baking pan or shallow bowl, whisk together the eggs and salt until combined and set aside.
In a separate third medium-sized baking pan or shallow bowl, mix the bread crumbs, salt, and pepper until combined. Set it aside.
Season the chicken cutlets on all sides with salt and pepper.
One at a time, dredge the chicken cutlets in the flour, then coat them in the egg mixture. Then coat them and press them down into the bread crumbs, ensuring the chicken cutlet is completely breaded. Repeat until the chicken cutlets are all breaded. You can place them on a platter or a sheet tray lined with parchment paper.
Add about ½ cup of oil to a large frying pan over medium heat and heat it until it reaches 350°. If you do not have a thermometer, sprinkle in some breadcrumbs, and if they fry but do not burn you're good.
Add in the breaded chicken cutlets, 1 to 2 at a time, and cook for 3 to 4 minutes per side or until golden brown and cooked through. Drain on a paper towel until ready to serve.
Salad: In a large bowl, toss together the arugula, microgreens, tomatoes, red onions, cheese, salt, and pepper, and keep it cool until ready to serve.
Next, in a medium-size bowl add in the lemon and honey and slowly drizzle in the olive oil while continuing to whisk until emulsified. Season the salad with salt and pepper and briefly set it aside.
Serve the cooked chicken Milanese with the salad on top and drizzle on the lemon vinaigrette.