Preheat the oven to 450°F (230°C). If your potatoes are not already cut, cut the 6 russet potatoes into 1/4-inch-thick matchsticks and pat them dry with paper towels.
In a large bowl, combine 2 tablespoons all-purpose (or gluten-free) flour, 2 teaspoons garlic powder, 1 teaspoon paprika, 1/4 teaspoon cayenne pepper, and a pinch or two of kosher salt and black pepper. Add the cut potatoes and toss until evenly coated.
Add 2 tablespoons extra virgin olive oil to the coated potatoes and toss again so the oil is distributed evenly.
Spread the potatoes in a single layer across two baking sheets (do not overcrowd the pans). Bake on the middle rack for 10–15 minutes, then use a spatula to flip the fries and bake another 10 minutes, or until the fries are golden brown and crisp. Watch closely toward the end—thin fries can brown quickly.
While the fries bake, make the Caesar-style dressing: in a jar or bowl combine 1/2 cup mayonnaise, 2 teaspoons lemon juice, 2 teaspoons Dijon mustard, 2 teaspoons Worcestershire sauce, 1–2 cloves garlic (grated), 1/4 cup grated Parmesan cheese, and salt and black pepper to taste. Whisk until smooth. If the dressing is too thick, add 1–3 tablespoons water, 1 tablespoon at a time, until you reach the desired consistency.
When the fries are hot from the oven, transfer them to a large bowl and toss immediately with 1/2 cup grated Parmesan cheese and 2 tablespoons chopped parsley or oregano. Taste and add additional kosher salt and black pepper if needed.
Arrange the dressed fries on a serving plate and drizzle generously with the Caesar dressing. Serve any remaining dressing on the side.