1. Preheat the oven to 375˚. Line two baking sheets with parchment paper.
2. Sift the flour, cocoa powder, salt, baking powder and baking soda into a large bowl. In the bowl of a standing electric mixer fitted with the paddle attachment (or using a handheld mixer), beat the butter, brown sugar, granulated sugar, and vanilla on high speed until light and fluffy, about 3 minutes. Reduce the mixer’s speed to medium and add the eggs, one at a time, beating until incorporated, about 1 minute.
3. On low speed, gradually add the dry ingredients and mix until just combined. Remove the bowl from the mixer and using a rubber spatula, mix in the chocolate and cherries by hand. Scoop by 2-heaping-tablespoonful amounts (or use a 2-inch diameter ice cream scoop) onto the prepared baking sheets. Moisten the hell of your hand and fingers with water and flatten the cookies until they are perfectly round, about ¼ inch thick and 3 inches in diameter. Place 6 cookies on each baking sheet, spacing them 1 inch apart. Bake the cookies until they are set in the center, 10-12 minutes, rotating the pans halfway through baking. Transfer the baking sheets to cooling racks to set for 5 minutes. Leave the warm cookies on the parchment paper and carefully slide them with the parchment paper off the baking sheet and onto cooling racks to cool completely. Let the baking sheets come to room temperature, line them with parchment paper, again, and repeat the steps for the second batch of cookies.
4. When all the cookies have cooled completely, you are ready to assemble the sandwiches. Allow the ice cream to soften until it is easy to scoop. Spoon ¼ cup onto half of the chocolate cookies and top with the remaining cookies to create sandwiches. Freeze on a baking sheet for 30 minutes. Serve immediately or wrap individually in plastic wrap and store in a freezer bag to serve later. The ice cream sandwiches will keep frozen for up to 2 months.