Preheat the oven to 300°F. Line the bottoms of two 12-by-18 inch sheet pans with parchment paper.
Combine half of the almonds with the half of the cornstarch in a food processor and pulse to grind into a fine, dry meal. Repeat with the remaining almonds and cornstarch. Doing this step in two batches helps prevent the release of oil and the formation of paste or nut butter. Purchased almond meal may also be used here as a substitute.
Combine the almond meal and powdered sugar in a medium bowl. Stir to mix and set aside.
Put the egg whites and cream of tartar in the bowl of a stand mixer fitted with the whip attachment. Beat on medium speed until they start to froth and then add about half of the sugar. When they start to become stiff, increase the speed to high and add the rest of the sugar. Beat until the whites start to lose their shine but still look wet. They will hang in stiff peaks when the whip is lifted from the bowl.
Fold about half of the almond mixture into the whites with a rubber spatula. Fold in the rest of the almond mixture just until no white streaks of egg whites remain.
Using a pastry bag fitted with a #1 tip, pipe 1-inch mounds of the batter onto the prepared pans, spacing them about 1 inch apart.
You may also drop the batter by tablespoonfuls rather than piping.
Bake on the middle shelves of the oven, rotating the pans 180 degrees halfway through the baking time, 35 to 40 minutes. After 30 minutes remove one of the cookies and check the bottom. If it is moist, cook for an additional 10 minutes. If it is smooth and dry, cook for an additional 5 minutes.
After the initial baking time, turn off the oven and crack the door slightly. Allow the cookies to dry in the oven for an additional 20 minutes. Remove from the oven and let cool completely on the pans on wire racks.
Store in an airtight at room temperature for up to 1 week.