Make the dressubg: In a jar, combine the red pepper flakes, garlic, vinegar, creme fra1che, mustard, olive oil, and maple syrup. Cover and shake until smooth, about 1 minute. Taste and add salt as needed. The dressing can be stored in the refrigerator for up to 2days.

Make the Milanese: Pat the chicken dry with paper towels, then slice each breast in half horizontally to make 12 thin pieces. Place the cutlets between two pieces of parchment paper and use a heavy skillet, rolling pin, or meat mallet to pound to about ¼-inch thickness.

In a large bowl, stir together the garlic, lemon juice, and olive oil. Add the chicken to the bowl and let sit at room temperature for 30 minutes, or cover and refrigerate for up to 4 hours (pull them out of the fridge 45 minutes before frying to come to room temperature).

Transfer the cutlets to a cutting board, letting the excess marinade drip off, then season with salt on both sides. In a shallow bowl, beat the eggs. Place the flour on a large plate. On a separate large plate, mix together the panko, Parmesan, and sesame seeds. Dunk each cutlet into the flour, shaking off any excess; then into the egg, letting the excess drip off; then into the breadcrumb mixture, pressing to adhere. Place each breaded cutlet on a baking sheet or large plate.

Line a separate baking sheet or large plate with paper towels. Fill a large skillet with about ¼ inch of neutral oil and heat over medium­high heat until it shimmers. Working in batches as needed, carefully add two or three cutlets to the oil and cook until deeply golden, 3 to 5 minutes per side. Transfer to the prepared baking sheet and immediately season with salt. Repeat with the remaining cutlets, adding more oil as needed between batches.

Place the arugula in a serving bowl. Lightly season with salt, then pour on the dressing and toss to coat. Finish with some pepper and Parmesan shaved with a vegetable peeler.