In a large pot, heat the olive oil or butter over medium heat. Once hot, add the diced Irish bacon. Cook until the bacon is crispy and golden brown, about 5-7 minutes. Remove the bacon from the pot and set aside on a paper towel.
Add the chopped onion and minced garlic to the pot with the bacon fat. Sauté for about 4-5 minutes until the onion is translucent.
Stir in the diced potatoes and pour in the chicken broth. Bring to a boil, then reduce heat and simmer for about 10 minutes until the potatoes are fork-tender.
Add the chopped cabbage and crispy bacon back into the pot. Season with salt and pepper. Simmer on low for an additional 5-7 minutes until the cabbage is tender.
Serve the soup hot in bowls, garnished with fresh parsley if desired.