Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper.
Make the sesame cucumber relish: in a small bowl whisk together the rice vinegar, sugar, toasted sesame oil, grated ginger, grated garlic, and 1/4 teaspoon kosher salt until the sugar dissolves.
Add the diced seeded cucumber, minced red onion, and 1 tablespoon toasted sesame seeds to the dressing and stir to combine; set aside to let the flavors meld.
Season the chicken cutlets on both sides with 1/4 teaspoon kosher salt and freshly ground black pepper.
Set up a breading station: place the flour on a shallow plate, the beaten egg in a bowl, and the panko mixed with shichimi togarashi, the remaining 1/4 teaspoon kosher salt, freshly ground black pepper, and 1 tablespoon toasted sesame seeds on a third plate.
Dredge each cutlet first in flour (shake off excess), then dip in the beaten egg, then press into the panko mixture to coat evenly.
Arrange the coated cutlets on the prepared sheet pan, spray lightly with olive oil spray, and bake for 20 minutes, rotating the pan halfway through cooking, until the coating is golden and an instant-read thermometer inserted into the thickest part reads 165°F (74°C).
To serve, top each chicken cutlet with about 1/2 cup of the sesame cucumber relish and drizzle 1 teaspoon soy sauce over each (plus sriracha if desired).