Heat the beer in a saucepan on medium-high heat. While the beer heating up, whisk together the cornstarch and warm water in a small bowl to make a slurry.
Once the beer comes to a rolling boil, let it continue to boil for about 5 minutes. Add the cornstarch slurry to the boiling beer, whisking constantly to fully incorporate it. Allow the beer to come back up to a boil, at which point the cornstarch slurry will slightly thicken the beer.
Turn the heat down to low. Cut the cream cheese into chunks, then whisk it into the beer until fully melted.
Add the shredded cheese a handful at a time, continuing to whisk until the cheese is fully melted before adding more.
Whisk in the Worcestershire sauce, Dijon mustard, salt, and pepper. Taste the cheese dip and adjust the salt or other seasonings to your liking.
Cover the cheese dip and keep the pot sitting over low heat so it stays warm and melted (or transfer it to a small chafing dish, crockpot, or electric fondue pot). Stir the cheese dip occasionally to prevent a thick skin from forming on the surface.