Preheat oven to 375F. In a large ovenproof skillet, heat olive oil over medium heat.

Add in onions gently cooking them until clear, about 10 minutes.

Turn up the heat to medium-high, add garlic, carrots, and celery.

Toss in mushrooms, mix well and cook until tender.

Add in the beef and rosemary, stirring in.

Season with a good pinch of salt and a teaspoon of pepper.

Continue tossing and quick fry for 3 - 4 minutes.

Stir in flour to coat then add in the Guinness and if needed, top up with enough water to cover.

Bring the mixture back to a simmer and cover with a lid or foil.

Place ovenproof pan in the 375F preheated oven, occasionally pull the pan out of the oven and stir a bit to mix it up. Return covered pan back to the oven and continue to cook for another hour, or until meat is very tender and stew is thick and dark-colored, about 1 1/2 hours.

If stew is still not thick enough, place the pan back on the stovetop and cook over medium heat until the sauce starts to thicken, stir frequently to prevent burning on the bottom.

Once ready, add in half the grated cheese, mix in well, season to taste, allow to cool for about 10 minutes.

On a flour-dusted surface, roll out puff pastry sheet evenly until about 1/8 inch thick. Then with a sharp knife, carefully and lightly make a criss-cross pattern over the top side of the Pastry without cutting through.

In an ovenproof deep dish, pour the stew in carefully and top with remaining grated cheddar cheese but do not mix in.

Place the pastry over the top of the pie dish, fold any overhanging edges back over the top edge or cut the excess off.

Brush the puff pastry top with the beaten egg wash.

Then continue to bake the steak and Guinness pie on the bottom shelf of the oven for an additional 30 - 45 minutes or until the pastry is puffed and golden.