Preheat oven to 350°F (175°C).
In the bowl of an electric mixer, beat 1 stick softened (not melted) butter and 2/3 cup sugar on medium-high speed until light and fluffy, about 2–3 minutes.
Add 1 large egg and blend, scraping down the bowl as needed. Mix in 1/4 cup cocoa powder until well combined.
Add 1 1/4 cups all-purpose flour, 1/2 tsp baking powder, and 1/4 tsp salt. Mix on low speed just until incorporated.
Fold in 1/2 cup mini chocolate chips and 1/2 cup Mallow Bits (mini marshmallows) with a spatula. The dough will be thick and dense.
Arrange the 28 graham cracker squares in a single layer on one or more baking sheets (do not overlap).
Using a spoon or small cookie scoop, place a spoonful of dough on the center of each graham cracker square. Slightly shape the dough to fit but do not completely cover the graham cracker — the cookies will spread a little while baking.
Bake at 350°F for approximately 10 minutes.
Remove the baking sheet from the oven. Immediately place one marshmallow half (from the 14 standard marshmallows cut in half, for a total of 28 halves) sticky side down onto the top of each warm cookie and press gently so it adheres.
Switch the oven setting to broil (low). Return the cookies to the oven and watch closely — broil only until the marshmallows reach your preferred level of browning (this can be under 90 seconds). Do not leave the oven unattended while broiling.
Remove the cookies from the oven and immediately place one unwrapped DOVE Chocolate Promise on top of each browned marshmallow so the chocolate starts to soften.
If you have more cookies to bake, set the oven back to 350°F and allow it a few minutes to return to temperature before baking the next sheet; repeat steps 7–11.
Store cookies loosely covered with a lid or covering that does not touch the tops of the cookies (the chocolate will remain soft and melty). Enjoy.