Heat the olive oil in a large pot over medium heat. Add the onion, carrots, and potatoes to the pot and season with 1 teaspoon of salt.
Pour in the beef broth, cover the pot, and bring to a simmer.
While the soup simmers, melt the butter in a small saucepan over medium heat. Whisk in flour and keep stirring for 1 minute to make a roux. Whisk in the milk a little at a time. Cook over medium-low heat, stirring frequently until the sauce is thick and creamy.
Stir the white sauce into the soup. Add the corned beef and allow to simmer for another 15 minutes
Stir in the Dubliner cheese and the cabbage. Cover and cook the cabbage for 3 to 5 minutes until tender but not mushy.
Portion the soup into bowls before serving warm.
Notes
If you can't find Dubliner cheese, sharp white cheddar cheese can be substituted.