Pit, chop, and dry the cherries until you have ½ cup. The cherries should be as dry as possible otherwise the dough will turn purple when you mix it.
In the bowl of a stand mixer with the paddle attachment, cream the butter and sugars until fully mixed and fluffy. Add in the egg and beat until combined, then mix in the amaretto and vanilla extract.
Add the flour, baking soda, and salt to the bowl and mix until just combined. Don't overmix!
Gently fold in the chocolate and cherries until just incorporated.
Scoop the cookie dough evenly into 12-14 balls and place them on the baking sheet. Chill in the fridge for at least 1 hour or covered overnight.
Preheat the oven to 350ºF and prepare a baking sheet with parchment paper.
Arrange the cookies at least 2 inches apart on the baking sheet, then bake for 12-14 minutes or until edges have browned but the centers are still gooey.
Use a large cup or round cookie cutter to scoot the cookies into even circles, then let them rest at room temperature for at least 5 minutes to finish baking.
Mix the powdered sugar and amaretto together to make the icing, then drizzle on top before serving.