Start by boiling a pot of salted water. Add the quartered baby red potatoes and cook for about 10 minutes, or until fork-tender. In the last 3 minutes, add the green beans to the boiling water. Drain the vegetables and set them aside.
While the vegetables are cooking, lay your chicken cutlets between two pieces of plastic wrap. Using a meat mallet or rolling pin, gently pound the chicken to about 1/2 inch thickness. Season both sides with Kosher salt and freshly ground black pepper.
In one shallow bowl, place the all-purpose flour. In a second bowl, beat the large egg. In a third bowl, add the seasoned Panko breadcrumbs. This three-step breading process is key to achieving that crispy texture.
Dredge each chicken cutlet first in the flour, shaking off the excess. Next, dip it into the beaten egg, ensuring it's fully coated. Finally, press it into the Panko breadcrumbs, making sure to coat both sides well.
In a large skillet, heat a generous amount of olive oil over medium heat. Once hot, add the breaded chicken cutlets, cooking them for about 4-5 minutes on each side, or until they are golden brown and cooked through. Use a slotted spoon to transfer them onto a paper towel-lined plate to drain any excess oil.
In the same skillet, add olive oil if needed along with the minced garlic. Sauté for about 30 seconds until fragrant. Add the drained potatoes and green beans, season with salt and pepper, and toss to combine. Cook for an additional 3-4 minutes until heated through.
Plate the crispy chicken schnitzel alongside the sautéed vegetables. Drizzle with fresh lemon juice, sprinkle with capers and chopped parsley, and serve with lemon wedges on the side for an extra zesty kick.