Cook the mozzarella sticks according to the package directions.
Meanwhile, melt the butter in a medium saucepan over medium heat. Whisk in the flour, mustard powder, smoked paprika and 1/2 teaspoons salt; cook, whisking, until smooth, about 1 minute. Whisk in the beer, half-and-half and hot sauce until smooth; bring to a simmer and simmer until slightly thickened, about 5 minutes. Remove from the heat and whisk in the Cheddar until melted.
Put the mozzarella sticks on a platter and drizzle with the sauce. Sprinkle with the everything bagel seasoning and chives.
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