Cook the Irish bacon: In a large pot or Dutch oven, cook the Irish bacon over medium heat until browned and crispy. Remove the bacon from the pot and set aside.
Soften the onion: In the same pot, add the butter and cook the chopped onion until softened.
Add the potatoes and cabbage: Add the chopped potatoes and cabbage to the pot and cook for 5 minutes, stirring occasionally.
Add the broth and thyme: Pour in the chicken broth and add the dried thyme. Bring the mixture to a boil, then reduce the heat and simmer for 15-20 minutes, or until the potatoes are tender.
Add the milk and cooked bacon: Stir in the milk or heavy cream and add the cooked Irish bacon back into the pot.
Season and serve: Season the soup with salt and pepper to taste, then serve hot.
Tips and Variations:
Irish Bacon Cabbage and Potato Soup Variations: