Preheat oven to 350°F. Line 2 baking sheets with parchment paper.
In a large bowl, beat butter, granulated sugar, and brown sugar on medium speed until light and fluffy, about 2 to 3 minutes.
Beat in eggs one at a time, then mix in vanilla and almond extract (if using).
In a separate bowl, whisk together flour, cocoa powder, baking soda, and salt.
Add dry ingredients to wet ingredients and mix on low just until combined; do not overmix.
Fold in chocolate chips and chopped dried cherries until evenly distributed.
Scoop dough into 1.5-tablespoon mounds and place 2 inches apart on prepared sheets.
Bake 9 to 11 minutes, until edges are set and centers look slightly soft.
Cool on sheets for 5 minutes, then transfer to a wire rack to cool completely.
Notes
For bakery-style thickness, chill the dough for 30 minutes before baking. Store cookies in an airtight container at room temperature for up to 5 days, or freeze for up to 2 months.