Prepare 2 baking sheets by lining with parchment paper.
In a medium bowl, whisk together flour, cocoa powder, salt and baking powder.
Melt the chocolate gradually over a bain marie or in a microwave. Cool slightly.
Using a stand mixer with the paddle attachment, begin mixing butter granulated sugar together until light and fluffy (2 - 4 minutes on medium speed). Scrape the bowl as needed.
Add eggs one at a time to bowl with butter and sugar. Mix on medium speed between each addition. Scrape sides of bowl as needed.
Add melted chocolate to mixing bowl. Mix on medium speed, scraping the side of the bowl occasionally, until the chocolate is well combined.
Add milk to the mixing bowl. Mix on low speed until combined.
Add flour mixture and mix on low speed until combined.
Scoop cookie dough onto the parchment-lined baking sheets using a cookie scooper (approximately 2 tablespoons per cookie). Leave approximately 2 inches of space between each cookie.
Bake cookies for 8 - 10 minutes, or until tops and edges of cookies are browning.
Let cookies cool on the baking sheets for 5 to 10 minutes, then transfer them to a wire rack to cool completely.
Assembling Ice Cream Sandwich Cookies
Slightly soften ice cream so it is easily scooped out of container.
Arrange half of the cookies on a baking sheet so flat side is showing.
Scoop approximately 3 tablespoons of ice cream on each cookie.
Place another cookie on top of the ice cream. Press gently to spread the ice cream to the edges of the cookie. Freeze until ready to serve.