Preheat your oven to 350°F (175°C). Line baking sheets with Silpat mats or lightly butter them; set aside.
In a medium mixing bowl, whisk together the flour, cocoa powder, baking powder, and salt. Set this dry mixture aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the softened butter, granulated sugar, and light brown sugar on medium-high speed until the mixture becomes pale and fluffy, about 4 minutes.
Add the eggs, one at a time, mixing well after each addition until fully incorporated. Mix in the vanilla extract.
Reduce the mixer speed to low and gradually add the dry ingredients. Mix just until the dough comes together—do not overmix. Chill the dough if it's too soft to handle easily.
Scoop out the dough in 2-tablespoon portions and roll each portion into a ball. Press a caramel or Rolo into the center of each ball, sprinkle the top of the caramel with a small pinch of coarse sea salt, then carefully wrap the dough around the caramel to fully encase it. Roll again to form a smooth ball.
Roll each dough ball in powdered sugar, coating generously. Place the cookies on the prepared baking sheets, leaving about 2 inches of space between each.
Bake in the preheated oven for 11 to 13 minutes, or until the cookies are cracked on top and just set around the edges. The centers will remain soft.
Let the cookies cool on the baking sheet for 5 minutes, then transfer them to a wire rack to cool completely. Keep in mind that the caramel centers will firm up as they cool, but the cookies are especially delicious served warm while the caramel is still gooey.