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1.
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Preheat the oven to 325 degrees F. Heat 2 tablespoons olive oil over medium heat in a large Dutch oven.
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Salt the brisket all over and sear on all sides until brown, about 10 minutes.
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Set aside.
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Add the onions and cook until tender, about 10 minutes, stirring occasionally to make sure the onions do not burn.
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Return the brisket to the pan and add the beer.
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Bring to a simmer, cover, and place in the oven.
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Braise until fork tender, about 3 hours.
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Let cool while making the potatoes and sauce.
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2.
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Boil the potatoes in a medium saucepan with salted water until fork tender, 15 to 20 minutes.
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Set 2 potatoes aside to cool and toss the rest of the potatoes with 1 tablespoon olive oil, a small handful of parsley leaves, roughly chopped, and season with salt.
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3.
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Pulse the remaining parsley leaves, the garlic, and anchovies in a food processor until roughly chopped.
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Leave the processor running while adding the remaining 1/2 cup olive oil in a steady stream.
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Peel the 2 reserved potatoes and add to the parsley along with the hard-boiled egg yolks and lemon juice and pulse 3 to 4 more times.
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Season with salt.
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4.
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Remove the brisket from the pan and slice against the grain.
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Degrease the braised onions.
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Spoon the braised onions on the bottom of the plate, and then add the sliced brisket.
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Top with the parsley sauce.
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Serve the potatoes on the side.
