Bring 2 medium pots of salted water to a boil.

Toss the whole Brussels sprouts into one pot for 5 minutes.

Toss the potatoes into the other pot for 10 minutes.

Drain both the Brussels sprouts and potatoes.

In a large saute pan with high sides, heat olive oil over medium high heat.

Add chorizo and cook for about 5 minutes, breaking it up as it cooks.

Add the minced garlic and diced shallots and cook for 3 minutes, until fragrant.

Season with a bit of salt and pepper.

Trim the bottom of the Brussels sprouts and cut in half.

Add the Brussels sprouts to the pan with the chorizo and cook for about 7 minutes, until they have started to brown.

Peel the skin off the potatoes, and cut into 1 inch cubes.

Toss the potatoes into the pan after the brussels sprouts have browned.

Season with a little more salt and pepper.

De-glaze the bottom of the pan with the beer, scraping up any browned bits.

Let the potatoes cook for about 5 minutes, until they start to brown a little bit.

Add more beer if necessary to make sure you get all the flavors off the bottom of the pan.

Cook your eggs in butter with a dash of salt in a separate pan, for about 2-3 minutes, just until the egg white is no longer runny, but the yolk still is.

Serve the egg over the hash while both are still piping hot! Enjoy.