In a large pot, heat olive oil over medium-high heat. Add leeks and celery and sauté for about 5 minutes.
Add cabbage, stir and cook for about 5 minutes.
Add chicken broth. Let simmer for about an hour over low heat.
Add 1/2 of the ingredients from the pot and 1/2 cup of the half and half cream to the blender. Blend in batches to prevent any hot soup from escaping the blender when blending. Blend to a smooth consistency and add to a large bowl.
Add the remaining contents from the pot and the remainder of the half and half cream to the blender and blend until smooth.
Pour all contents from the blender and bowl into the pot and let simmer for 10 minutes.
Sprinkle with kosher salt and freshly cracked pepper.
For toasted Irish soda bread, thinly slice bread on a diagonal. Place bread onto a cookie sheet, sprayed with non-stick cooking spray and bake for 5-7 minutes in a preheated oven at 375 degrees, or until lightly brown.
Ladle soup into bowls, serve with toasted Irish soda bread and garnish if desired.