I take the dried cherries and rinse them off with cold water, just a quick swirl to separate any cherries stuck together. Don't let them soak. I drain them in a colander and then dry them on a paper towel.
In a bowl, weigh or measure the light brown and white sugars. In another bowl, weigh or measure the flour, baking soda, baking powder, and salt, running a whisk through to blend.
Blend the butter and cream cheese on a medium mixer speed. Add the sugars and continue mixing at medium speed until they are light brown, for about 2 to 3 minutes. Add the vanilla extract and (optional almond extract). Turn the mixer to low and gradually incorporate the flour mixture until all the flour mixture is blended.
Turn the mixer off so you can scrape down the sides. Add the dried cherries and white chocolate chips and blend for 10 seconds. You may have to mix by hand to spread the cherries and white chocolate chips evenly throughout the cookie dough. Cover lightly and put into the refrigerator for half an hour.
Preheat the oven to 350°F (175°C or 180°C)—line 2 cookie pans with parchment paper. I use a medium cookie scooper to place 12 mounds onto the prepared sheet pan. Then, I put a square piece of parchment paper on top of the cookie mound. Using a flat-bottom drinking glass, press lightly on the top of the parchment paper to flatten the cookie mound to about ½" thick. They bake more evenly this way since they do not spread. Bake for 11-13 minutes. Then, move them to a cooling rack after taking them from the oven.