Preheat oven to 375°F.
Line a rimmed baking sheet with parchment paper.
Heat EVOO, a turn of the pan, in a medium skillet over medium to medium-high heat. Add celery, onion, carrot and garlic, season with salt and pepper, and sauté to soften, 10 minutes, stirring frequently. Pour in beer and stir. Let beer reduce by half. Turn off heat and let cool.
Meanwhile, soak the bread in milk and grind the corned beef in a food processor, pulsing to finely chop. Place corned beef and ground beef in a bowl and add cheese. Wring out the bread and add it to the meat, crumbling it into small crumbs over the bowl. Add veggies and beer then season with salt, pepper, mustard, cayenne and Worcestershire. Add eggs then mix with your hands to combine.