Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone mats and lightly spray if desired.
Measure the flour by lightly spooning it into the measuring cup and leveling with a knife. Sift the flour with the baking soda and 1/4 teaspoon salt into a bowl and set aside.
Melt the butter in a large saucepan over medium heat. Remove from the heat, then stir in the cocoa powder, granulated sugar, and brown sugar until the mixture resembles coarse sand.
Stir the yogurt and vanilla into the chocolate mixture until combined, then add the sifted flour mixture and mix until a moist dough forms.
Wrap portions of the chocolate dough around each caramel ball, sealing the caramel completely; roll into smooth balls and place on the prepared baking sheets about 2 inches apart.
Lightly sprinkle each cookie with a pinch of sea salt.
Bake for 10–12 minutes, until the cookies are almost set. Let cool on the baking sheets for 2–3 minutes, then transfer to a wire rack to cool completely.