Pour beer into a saucepan and simmer uncovered for 5 minutes, then transfer to a 6-quart slow cooker. Add onion, celery, carrot, broth, salt and pepper.
Cover and cook on low for 4 hours until vegetables are very soft. Blend the base briefly with an immersion blender until mostly smooth.
Turn the cooker to high and stir in milk. Mix cornstarch with cold water and stir the slurry into the soup, then cover and heat for 25 to 30 minutes until the liquid bubbles lightly and thickens.
During that final stage, heat the oven to 375°F. Toss bread cubes with olive oil on a rimmed sheet pan and bake for 12 to 15 minutes, turning once, until crisp.
Switch off the cooker and wait for bubbling to stop. Stir in cheddar in 4 additions, then Dijon and Worcestershire, until smooth.
Divide among 6 bowls and add one-sixth of the croutons to each just before serving.