In a medium pot, whisk cornstarch and ½ cup milk until smooth. Add lager and remaining ½ cup milk, stir to combine, and bring to a boil over medium-high heat. Cook, stirring occasionally, until thickened, about 1 minute. Whisk in mustard, Worcestershire, and paprika until combined.
Reduce heat to low. Add cheese and stir until melted and incorporated; season with salt, if needed.
Transfer dip to a serving bowl. Top with chives. Serve with pretzels alongside.
