In a large soup cover the cubed potatoes with cold water just until the potatoes are completely covered. Lightly salt the water. Let the water come to a rolling boil, and then turn down the heat just a bit so it doesn't bubble over. Continue cooking the potatoes until they're fork tender, or about 20-25 minutes. Strain the potatoes, run under cold water for 30 seconds, and then transfer to the bowl of a stand mixer. Add 2 tablespoons of the butter and 1/3 cup heavy cream to the mixing bowl. Use the whisk attachment to whip them until they've reached the desired mash. Cover the mixing bowl with foil to keep warm until you are ready to serve.

Melt the butter over medium heat in a large skillet. Add in the flour and cook, whisking constantly, for 2-3 minutes or until golden (this allows the four taste to cook out). Whisk in the beer and broth and continue whisking until no clumps remain and the sauce begins to thicken. Season with salt and black pepper, to taste. Bring the sauce to a boil over medium high heat and then reduce the heat to a simmer and let the gravy cook, stirring occasionally, for about 5-6 minutes. Whisk in the mustard and remaining 1/3 cup of heavy cream. The gravy should be thick and creamy, nicely sticking to and coating the back of a spoon, and will taste subtly like the beer you add to it. If the beer taste is too strong, you may add a teaspoon or two of sugar to balance out the bitterness.

Pour a liberal amount of gravy over a serving of the mashed potatoes and serve them as a side with any traditional Irish meal, or pair them with chicken, grilled meats, or burgers.