Toast the almonds on a baking sheet in the oven until they are golden brown, about 10 minutes. Cool and then coarsely chop, either by hand or in a food processor.
Put the egg whites in the bowl of a stand mixer and add the salt. On the second highest speed of the mixer, beat the egg whites until they come to medium peaks. With the mixer running, gently sprinkle in the sugar and cinnamon. Beat until stiff peaks form, then remove the bowl from the mixer. Gently fold in the chopped almonds in 3 additions.
Drop the batter in 1-inch balls, onto 2 parchment-lined cookie sheets. Bake until light brown all over, firm to the touch, and they lift cleanly off the baking sheet, 35 to 40 minutes, rotating the pans halfway through. Remove from the oven and cool on the baking sheets. These cookies can be stored in an airtight container for up to a week.
Cook's Note: Try to avoid baking these cookies on a wet and humid day as the crisp exterior of the cookie will slowly melt into something soft and sticky.