This is one we won't be going with exacting ingredients for. Instead we will look at what was used to make the meal.
Beer (tradition would call for a Guinness or a Smithwicks but its always great with a good beer you have on hand)
large dice the veggies. Sear the brisket to develop a hard sear (a nice crust). Remove the brisket from the pan and saute the carrots, onion, and garlic till the onion begins to turn translucent. Deglaze with the beer then add the brisket, potatoes, and cabbage to the pan. Add water till it comes up at least 75% of the brisket (more is ok). Bring to a boil then reduce heat, cover and allow to simmer for 2.5 to 3 hours.
Time for a pint...