Scatter the potatoes on a baking sheet and toss with the grill seasoning and EVOO. Roast in the oven, turning occasionally, until they are golden brown and tender, about 40 minutes.
While the potatoes are roasting, place a medium pot over medium heat with the butter. When the butter has melted, sprinkle the flour over the top and cook for about a minute. Whisk the milk into the butter-flour mixture and simmer until thickened, 2-3 minutes.
Remove the pot from the heat and whisk in the cheese and horseradish until the cheese has melted. Season the sauce with salt and pepper, and reserve warm.
Serve the oven fries with a small bowl of cheddar-horseradish dipper alongside.