If using wooden skewers, soak them in water for about 30 minutes to prevent burning on the grill.
In a large bowl, whisk together olive oil, minced garlic, oregano, thyme, salt, and pepper. Add the chicken pieces and toss until well coated.
Add parmesan cheese and breadcrumbs to the bowl. Mix gently to coat the chicken pieces. The parmesan will add a savory crust as it cooks.
Thread the chicken pieces onto the skewers, leaving a little space between each piece for even cooking.
Preheat your grill to medium-high or preheat your oven to 425°F (220°C) if you prefer roasting. Lightly oil the grill grates or a baking sheet.
Grill: Cook the skewers for about 8–10 minutes, turning halfway, until the chicken reaches 165°F (74°C) in the center and is nicely charred in spots.
Oven: Arrange skewers on a lined baking sheet. Bake for 12–15 minutes, then broil for 2–3 minutes to get a bit of browning on top.
Remove from heat, sprinkle with chopped parsley if using, and let rest for a couple of minutes before serving.