Fill a pot about halfway full of water. Bring it to a simmer over low heat. Find a heat-safe bowl (glass or stainless steel) that can be set into the pot of simmering water. Make sure the bottom of the bowl is not touching the water. The steam is what will melt the butter and chocolate.
Add the butter and semisweet chocolate chips to the heat-safe bowl. With the heat on low, use a rubber spatula to stir the chocolate until it is melted and smooth. This takes about 5 minutes.
To the bowl of a stand mixer fitted with the paddle attachment, add eggs and 1 ½ cups sugar. (Reserve ½ cup sugar for rolling the dough.) Beat on medium speed until combined. Add in the vanilla and melted chocolate and beat until combined, stopping to scrape the sides of the bowl as needed.
Add in the flour and baking powder and mix until combined.
Gently fold in the milk chocolate chips.
Cover the bowl of cookie dough and store it in the refrigerator for one hour.
When ready, preheat the oven to 350°F and line baking sheets with parchment paper.
Using a 2-tablespoon scoop, drop the cookie dough onto the lined baking sheets. Roll each ball of dough into the reserved granulated sugar and place back onto the lined baking sheet, leaving about 2 inches between each.
Bake for 17 minutes, or until the edges appear dry.
Let the cookies cool for about 10 minutes on the baking sheets before enjoying them.