In the bowl of a stand mixer fitted with the paddle attachment, beat the butter, granulated sugar, and brown sugar on medium speed until light and fluffy, about 2 minutes. Scrape down the sides of the bowl. Add the egg and beat until fully incorporated.
Sift the flour, cocoa powder, baking powder, baking soda, and salt into the bowl. Mix on low speed just until the dry ingredients are fully absorbed and a cohesive dough forms. Do not overmix. Add the chopped milk chocolate and mix briefly until evenly distributed. Cover the bowl and chill the dough for 20 minutes.
Heat the oven to 350°F/175°C. Line a baking sheet with parchment paper.
Using a cookie scoop or tablespoon, portion the dough into 15 balls (about 1.4 ounces/40 grams each). Flatten each ball slightly, press a white chocolate praline or square into the center, then wrap the dough around it and roll into a smooth ball.
Arrange the balls on the prepared baking sheet, spacing them about 2 inches apart. Bake until the edges are set but the centers are still soft and slightly puffed, 9 to 10 minutes. The cookies will appear underbaked but will continue to set as they cool.
Let the cookies rest on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely. Serve once the centers have firmed up slightly but are still gooey.