Melt the butter in a saucepan over medium heat. Add the flour and whisk into the butter, as if making a roux. Cook until the texture changes, but don't allow the mixture to begin to brown.
Remove from the heat. Add the milk and whisk until you have a thick bechamel, the texture of loose mashed potatoes. Add the salt, white pepper, and nutmeg.
Wash the spinach well but leave dripping wet. In a saucepan over medium-low heat, covered, cook the spinach until just tender. Remove the spinach from the pan. Squeeze out any excess water. Chop in a food processor, or by hand.
Stir the spinach into the bechamel until well blended.
Whisk the egg yolks and the vinegar briskly in a metal bowl set over a saucepan with about an inch of simmering water at the bottom. If you see even a hint of curdling in the eggs, take the bowl off the heat, but keep whisking. Keep going back and forth from the heat until the mixture turns thick and lightens in color. Whisk in a tablespoon of warm water.
Begin adding the softened butter, a pat at a time. After about a fourth of the butter is in there, you'll begin to see a change in the texture of the sauce. At that point, you can step up the addition of the butter a bit, and keep going till all the butter is incorporated.
Whisk in the cayenne and the lemon juice. Set the bowl in a bigger bowl of warm (not hot!) water and cover with plastic wrap.
Use a large stainless-steel skillet filled with water about an inch and a half deep. Bring it to a boil while dissolving the salt into it and adding the vinegar.
The hard part of poaching eggs is keeping them together as you add them to the pan. The best trick is to use a coffee cup--the kind that narrows at the bottom. Break one egg into each of four cups. (Or eight, if your skillet is big enough to fit all those eggs.)
When the water comes to a boil, lower the heat to the lowest possible setting. Slide the eggs carefully into the pan, two (or four, even) at a time. Let them simmer for three to four minutes, depending on the size of the eggs.
The best tool to remove the eggs with is a round skimmer with holes in it, or a large slotted spoon. Carefully remove one at a time, and let the excess water drip off.
Place about two tablespoons of creamed spinach into each artichoke bottom, making a depression in the center of the spinach. Slide a freshly-poached egg atop the spinach, then top with hollandaise. Repeat for all the other artichoke bottoms, two to a plate.Serves four