Wash and scrub the potatoes well, leaving the skins on for extra texture. Slice each potato lengthwise into evenly sized wedges.
Place the wedges in a bowl of cold water for about 20 minutes to remove excess starch. Drain well and pat them completely dry with paper towels.
In a large bowl, combine the cornstarch, garlic powder, paprika, onion powder, oregano, thyme, salt, and black pepper. Toss the potato wedges until evenly coated.
Heat about 3 inches of oil in a deep pot to 350°F (175°C).
Fry the wedges in small batches for about 5 to 6 minutes until they are lightly cooked but not deeply browned.
Remove them to a wire rack and let them rest for 5 minutes.
Increase the oil temperature to 375°F (190°C). Return the wedges to the hot oil and fry for another 2 to 4 minutes until crisp, golden brown, and cooked through.
Transfer the fried wedges to a paper towel-lined plate or wire rack. Sprinkle immediately with additional salt, Parmesan cheese, Cajun seasoning, or chopped parsley if desired.
Serve immediately while hot with your favorite dipping sauces.