Preheat oven to 425°F (218°C). Place a rack in the center of the oven. Line a baking sheet with parchment paper and slick the paper with olive oil.
In a small bowl, whisk together the cornstarch, chili powder, paprika, cumin, chili flakes if using, cayenne, and salt.
Rinse the potatoes under cool running water and peel them. (You can leave some skin on the potatoes if you want to go for a more rustic feel.) Using a sharp knife, slice a 1/4 -inch piece off each potato lengthwise. This gives you a stable base. Rest the potatoes, cut side down, on your work surface and slice them into 1/4- to 3/8-inch planks. Stack the planks in piles, 2 to 3 planks high, and slice the stacks lengthwise into 1/4- to 3/8-inch strips. Look at that! French fries!
In a medium bowl, toss the potatoes with the oil, Worcestershire sauce, and grill seasoning mix. Sprinkle the cornstarch mixture over the fries and, using tongs, toss them together, making sure that every potato is well coated. Spread the fries on the prepared baking sheet in a single layer. (For the crispest results, make certain the fries don't touch one another. If you need a second baking sheet, so be it.)
Bake the fries, removing from the oven 2 or 3 times to toss them and then rearrange them in a single layer, until the potatoes reach the desired crispiness, 30 to 40 minutes.
Remove the baking sheet from the oven, scatter the Cheddar over the fries, and then return them to the oven for just a few minutes to melt the cheese. Slide the chili cheese fries onto a platter, sprinkle with chives, and serve immediately.