Mix dry ingredients: In a small bowl, stir together the flour, milk powder, baking powder, baking soda, and salt. Set aside.
Cream butter and sugars: In a large mixing bowl, use an electric hand mixer to beat softened butter until creamy, about 3 minutes. Add granulated sugar and brown sugar and beat together well until creamy and fluffy, another 3 minutes.
Add wet ingredients: Add the egg, miso paste, and vanilla extract. Beat again until combined.
Add dry to wet mixture: Add the flour mixture and mix on low speed until almost combined with some flour patches remaining.
Add chocolate: Add the chopped dark chocolate and finish mixing the dough by folding it together with a spatula.
Scoop and chill cookie dough: Line a cutting board with parchment paper. Use a 4-tablespoon cookie scooper to scoop the cookie dough. Release the dough balls on the parchment paper. No need to leave space between them. Place the whole board in the fridge to chill for about 30 minutes until the dough is firm.
Prep: Preheat the oven to 350°F and line a baking sheet with parchment paper.
Make cavity: Take a cookie dough ball and use your second knuckle or thumb to press a depression in the middle. Insert your thumbs and pinch the dough to thin it out and make a bigger cavity.
Insert caramel candies: Place one caramel candy into the cavity. Press the dough together around the caramel to close and seal the hole. Place the dough ball with the sealed side down on your lined baking sheet. Repeat with the rest of the dough balls.
Bake: Bake cookies for about 12 minutes until the edges are set but the cookies are still very soft. About 2 minutes before they finish baking, press a few chocolate chunks on top of each cookie for picture-worthy cookies (optional).
Reshape: Immediately after baking, swirl the cookies around in a round cutter or bowl that's slightly bigger than the cookies or use a fork to push any uneven edges in for perfectly round cookies (optional). Sprinkle each cookie with flaky salt.
Let cool: Let the cookies cool on the baking sheet for about 15 minutes before carefully (they will still be very soft) transferring them to a wire rack to cool completely.