Preheat the oven to 200 F. Position racks in the upper and lower thirds of the oven.

In a clean, dry bowl place the egg whites with the cream of tartar. Using a whip attachment, beat at medium high speed with a stand mixer or high speed with a hand mixer until the egg whites are creamy white and hold a soft peak. Continue to beat, adding a little sugar at a time, until you've used all the sugar. This should take 1 1/2 - 2 minutes, until the whites are very stiff.

Sprinkle the salt and the finely chopped chocolate over the stiff egg whites. Gently fold the chocolate into the egg whites.

Drop heaping teaspoons of batter 1 1/2 inches apart on a parchment-lined baking sheet. You may also choose to pipe the batter, but I am not that fancy (and I paid for it too as my chocolate meringues are all sorts of crazy shapes). Sprinkle the dropped batter with the grey sea salt to taste.

Bake for about 2 hours, rotating the pans front to back and top to bottom halfway through. Remove a test cookie and let it cool completely--warm meringue cookies are apparently always soft. You are testing for crispiness. At such a low temperature, the remaining cookies will not burn while they wait for your test. If the cookie is not completely crisp (it should not be chewy or stick in your teeth at all), continue baking and test at 15-20 minute intervals.

When the cookies are crisp, turn the heat off and let them cool in the oven. If you have a new oven, like me, it may take forever for them to cool; I took them out after about 1 1/2 hours, when the pans were still warm and let them cool on my counter.

Cool completely before storing but do store in an airtight container immediately after cooling. I won't claim they store indefinitely (Medrich says several weeks) but they definitely store well.