Preheat the oven to 250°F. Place a wire rack on top of a baking sheet and keep handy.
Split each chicken breast in half horizontally to create two thinner pieces of chicken. I like to do this by carefully placing my hand on top to give myself a feel for whether or not I am slicing the chicken evenly. With a meat mallet or rolling pin, gently pound the chicken VERY thin—about 1/4-inch thick. To keep things tidy, place a sheet of plastic wrap or wax paper on top prior to pounding. Sprinkle both sides of the chicken with 1 teaspoon of the salt.
Set up your dredging stations: Place the flour in a wide, shallow dish (a pie dish works well). Beat the eggs in a second shallow dish. In a third, combine the breadcrumbs, garlic powder, and onion powder.
Dredge the chicken: With tongs, grab one end of a piece of chicken, and dip in the flour, then the eggs, then the breadcrumbs, coating both sides of each piece of chicken and shaking off excess as you go. Transfer to a clean plate. Repeat with the remaining chicken.
Place the arugula in a large bowl. In a small bowl or a liquid measuring cup with a spout, whisk together the olive oil, lemon juice, 1/4 teaspoon pepper, and remaining 1/4 teaspoon salt. Pour enough dressing on the arugula to moisten it. Toss to combine, reserving the extra dressing for serving.
Cook the chicken: In a large skillet, heat 2 tablespoons of the canola oil over medium heat. Once the oil is hot, carefully lower two of the breaded chicken pieces into the skillet, ensuring that they are not touching. Cook on the first side until golden, about 3 minutes. Flip and cook on the other side until it is golden brown and the chicken is cooked through, about 2 minutes more. Transfer to the prepared baking sheet. Immediately sprinkle the top of the chicken with a small pinch of salt, then place in the oven to keep warm. Repeat with the remaining 2 chicken pieces, adding the remaining tablespoon canola oil to the skillet as needed to prevent sticking. Serve each chicken Milanese piece hot, with a pile of the arugula and lemon wedges along side.
Notes
TO STORE: Refrigerate leftover chicken Milanese in an airtight container for up to 2 days.
TO REHEAT: Rewarm leftovers on a baking sheet in the oven at 350 degrees F or in the microwave.
TO FREEZE: Freeze chicken Milanese in an airtight, freezer-safe storage container for up to 3 months. Let thaw overnight in the refrigerator before reheating.