Preheat the oven to 350°F. Line two baking sheets with parchment paper or silicone baking mats.
In a medium bowl, sift together the flour, cocoa powder, baking powder, and salt.
In the bowl of an electric mixer, beat the butter, brown sugar, and granulated sugar on medium-high speed until well combined and smooth. Add the egg, egg yolk, and vanilla and beat until combined. On low speed gradually add the flour mixture. Fold in the chocolate chips with a rubber spatula.
Using a medium cookie scoop, drop the dough by 1.5 tablespoon rounds onto the prepared baking sheets. Using the cookie scoop, press indentions into the cookies to allow for the topping at the end. The indentions can be made before they are cooked or after they come out of the oven.
Bake for about 10 minutes, or until the cookies are set. Let cool on baking sheets for 10 minutes before removing the cookies to wire racks to cool completely.
For the topping: In a small saucepan set over medium heat, combine the milk, sugar, egg yolk, and butter. Cook, stirring frequently, until the mixture has thickened, about 10 minutes. Remove from heat and stir in the vanilla, coconut, and pecans. Let cool until thick enough to spread on top of the cooled cookies.
Drizzle the melted chocolate all over the cookies. Drizzle the melted chocolate all over the cookies. (To melt the chocolate chips, put them in small bowl and microwave for 30 seconds before stirring. Microwave for 15 more seconds and stir again until smooth.)
Let everything set for at least 15 minutes before serving. Cookies are best served the day they are made.