Combine half of the chocolate, the butter, and vegetable oil in the top of a double boiler placed over simmering water, stirring until the chocolate is melted and the mixture is smooth. Remove from the heat and set aside to cool.
Whisk together the flour, baking powder, and salt in a small bowl to combine. Whisk together the eggs, brown sugar, and vanilla extract in a medium bowl. Gradually add the melted chocolate mixture to the egg mixture, whisking until well combined. Gently fold the flour mixture into the batter, mixing just until combined. Fold in the remaining chocolate. Cover the dough with plastic wrap and chill in the refrigerator for at least 1 hour, or overnight.
Preheat the oven to 350°F and line two baking sheets with parchment paper. Using a small ice cream scoop, spoon 10 balls of batter onto each baking sheet. Bake for 12 to 14 minutes, until the tops are dry and cracked. Remove from the oven and let cool for 5 minutes. Transfer the cookies to a wire rack and let cool completely.
Spread the filling on the flat side of half of the cookies. Place another cookie, flat side down, on top of the filling and press down gently.