In a medium mixing bowl, whisk to combine the flour, cocoa powder, baking soda, and salt.
In the bowl of a stand mixer fitted with the paddle attachment (or in a large bowl, using a handheld electric mixer), cream the butter, light brown, and granulated sugar on medium speed for about 3 minutes until lightened in color and fluffy.
Add the egg and vanilla and mix on low speed for 30 seconds, just until combined.
With the mixer on low speed, gradually add the flour mixture a few tablespoonfuls at a time, mixing just until combined between each addition. Add the chocolate chips and chopped chocolate and mix on low speed just until combined.
Scoop cookies to be about 1½ tablespoons in size (about 35g each) with a triggered cookie scoop or two spoons, onto parchment-lined baking sheets, leaving about 2 inches of space between each cookie.
Bake for about 9 minutes. Remove the pan from the oven and tap the cookies on the counter once to flatten the tops (this gives a flat surface for the frosting.) Let them cool on the pan for 5 minutes, then transfer to a cooling rack to cool completely.
For the Frosting:
In a small saucepan, whisk to combine the sugar, milk, and egg yolk. Add the butter and salt. Cook over medium heat, stirring frequently with a silicone or rubber spatula for about 5 minutes, until the butter melts and the mixture comes to a low boil. Once at a low boil, cook for 1 more minute, stirring frequently until the mixture coats the back of a spoon. Remove from heat.
Stir in the coconut, chopped pecans and vanilla extract. Let the frosting cool completely, stirring occasionally. (To cool faster, transfer the mixture to a bowl and place in the refrigerator, stirring occasionally.)
Dollop about 1 tablespoon on each cooled cookie and spread almost to the edges.
In a microwave-safe bowl, heat the chocolate on on high heat in 30 seconds, then stir (if possible). Continue to heat in 15 second increments, stirring in between each, until melted. Drizzle the chocolate over top of the cookies.
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Notes
Weigh the flour. Use a kitchen scale to weigh the flour so you don’t accidentally use too much, which will cause the cookies to dry out. If you don’t have a scale, fluff the flour in its container, spoon it into your measuring cup, and level off the top with a knife.
Use room temperature ingredients. Set the egg and butter out in advance so they are easier to incorporate into the cookie dough. See my tutorial for how to soften butter quickly if you forget to set it out.
Chocolate substitution: You can use 1 cup of semi-sweet chocolate chips (180g) in place of the ½ cup of chocolate chips and 4 ounces of chopped German chocolate bar.
Use a triggered cookie scoop: This will ensure all the cookies are the same size.
To cool the frosting faster: Transfer the frosting to a bowl and pop it into the refrigerator. Stir occasionally.
Use a piping bag for the chocolate drizzle. The melted chocolate can be a bit finicky to drizzle neatly without one. You can also put it in a Ziplock bag and snip off one corner.