Pre-heat the oven to 375°F.
In a large, ovenproof pan fitted with a lid, heat 2 tablespoons of the butter, over medium-low heat.
Add the onions and garlic and cook, stirring frequently, until soft; about 10 minutes.
Add the carrots, celery, mushrooms and remaining 2 tablespoons butter and cook over medium heat, stirring frequently, until the mushrooms are dark in color and the moisture released by them has evaporated; about 15 minutes.
Season the beef pieces all over with salt and pepper.
Add the beef, flour and rosemary to the pan and cook, over high heat, stirring often, for about 5 minutes.
Add enough Guinness to just cover the beef.
Cover the pan and put it in the oven for 1-1/2 hours.
Remove from the oven and stir; return to the oven and cook for 1 hour more.
If it remains thin, set the pan over medium-low heat, remove the lid and reduce the liquid.
Once cooked, season to taste with salt and pepper; add in about 1/2 of the cheddar.