Mill your sugar (3 C + 1/4 C Finely Ground Sugar) in either a food processor or coffee mill to get that finely ground sugar to keep the cookie light.
Set aside, separating 1/4 C of sugar for coating cookies before baking)
Now fill one bowl with the confectioner's sugar and then set it aside for coating cookies as well.
In a food processor, chop/grind the cherries and set them aside.
Preheat oven to 325° F
Prepare baking trays with silicone baking mats.
In a small bowl combine flour, baking powder, and baking soda, set aside.
Large Mixing Bowl or Stand Mixer
Combine egg whites* and tartar sauce.
Mix to stiff, without over-mixing.
Once egg whites are stiff it's time to add in the other ingredients by hand.
Fold in: sugar, salt, almond extract, Amaretto, and then the flour mixture.
Using a rubber scraper initially to incorporate all ingredients.
Next, fold in the almonds and the cherries and distribute evenly without over-mixing.
Then create a mound.
Using a teaspoon, create a scoop and place it in your hand, rolling to a 1" ball. (or use a cookie scoop)
Take each ball and roll quickly and lightly through sugar mixtures.
First into the very light milled sugar, then into the powdered sugar.
Place each ball onto the tray, spacing about 1" apart and lighting depressing ball into a slightly pressed cookie.
Just lightly press on each, enough that the cookie will crack while baking.
Place tray on the bottom rack, and allow it to bake without OPENING the oven to prevent temperature loss.
Bake for 20-24 minutes, the tops will crack further and may appear moist, but the bottoms will be just very lightly brown, take them out.
Allow these amaretti to SIT On the silicone matted baking tray for at least 5 minutes to let them set up.
*OPTIONAL: For those that prefer an all crunchy cookie, let them bake 5 minutes past this timing.
Next transfer cookies to the cooling tray for at least 15 minutes.
Store in an airtight container for up to a week.
I doubt they will last that long.