Whisk together the brown sugar and white sugar -- you might need to mash it with the back of a spoon to make sure there aren't any lumps.
Whisk in the egg whites, canola oil and vanilla extract.
Sift the flour over the batter mixture and stir until flour is fully incorporated into the batter.
Set the batter aside for 20 minutes.
Line 2 large baking sheets with parchment paper and preheat the oven to 350 °F
Drop 1 measured tablespoon of batter onto the baking sheet. Use the back of a spoon to spread the batter around in a 3-inch-wide circle.
You'll be able to fit about 8 or 9 3-inch-wide batter circles on each baking sheet.
Pop each baking sheet in the 350 °F oven for about 5 minutes, until the edges of the cookies are lightly brown.
Immediately remove each cookie from the baking sheet with a large spatula. Working very quickly, fold the cookie in half to make a half-circle. Then, fold the half-circle in half crosswise.
Immediately place in cookie in a muffin pan cavity so it can hold its shape while it cools.
If the cookies become soggy, you can re-crisp them by putting them in a 275 °F oven for a few minutes.