Heat 2 tablespoons of cooking oil in a Dutch Oven and add diced carrots, onion, celery, and peppers. Cook on medium heat until vegetables are tender, add garlic and cook for an additional 1-2 minutes, or until garlic is fragrant.
Remove vegetables from pot, turn pot on low and add ⅓ cup butter. When butter is melted sprinkle in flour and whisk continually to form a roux. Cook the roux for 3-5 minutes while whisking.
Slowly add Half and Half to the roux, whisking to combine. Then add chicken stock and beer.
Add Cheddar cheese one handful at a time until it is completely melted into the soup.
Mix in mustard, Worcestershire sauce, seasonings, and return vegetables to the pot.
Bring the pot to a simmer for 5 minutes and serve the hot soup topped with bacon or chives, as desired.