In a small saucepan off heat, whisk together the granulated sugar, dry mustard powder, cornstarch, paprika, ground turmeric, garlic powder, onion powder, cayenne pepper, and kosher salt until evenly combined.
Whisk in the water and distilled white vinegar until smooth, then let the mixture stand 5 minutes to hydrate the mustard.
Set the pan over medium heat and cook, stirring constantly, until the sauce comes to a simmer and thickens to a glossy, spoon-coating consistency, 3–5 minutes.
Remove from heat, taste, and adjust with a pinch more salt or a splash of vinegar if needed. Transfer to a clean jar and let cool at room temperature for 15–20 minutes.
Cover and refrigerate until fully chilled and the flavors meld, at least 1 hour (up to 24 hours). The sauce will thicken as it chills; stir and thin with 1–2 teaspoons water to reach a nugget-dipping consistency, if desired.
Serve cold with chicken nuggets, fries, or sandwiches. Store refrigerated up to 2 weeks.