Corned Beef Hash and Poached Eggs with Easy Hollandaise

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Hollandaise:

2 egg yolks

1 teaspoon dry mustard

Pinch cayenne pepper

2 tablespoons water

1 cup (1/2 pound) unsalted butter, melted

1/2 lemon, juiced

Kosher salt and freshly ground black pepper

2 tablespoons extra-virgin olive oil

2 tablespoons unsalted butter

1 onion, chopped

2 cups chopped corned beef

2 cups chopped Herbed Root Vegetables, recipe follows

2 tablespoons chopped fresh chives, plus more for garnish

4 eggs

2 tablespoons white vinegar

Herbed Root Vegetables:

2 tablespoons extra-virgin olive oil

2 tablespoons unsalted butter

1 pound new potatoes, scrubbed

1 pound baby carrots, trimmed and scrubbed

1 pound baby turnips, trimmed and scrubbed

1 pound baby parsnips, trimmed and scrubbed

Kosher salt and freshly ground black pepper

Herb Butter: 

1/2 pound unsalted butter, softened 

1/2 cup mixed chopped fresh herbs like thyme, mint, chives, parsley, or chervil 

Kosher salt and freshly ground black pepper