Preheat oven to 375 degrees F (190 degrees C). Line baking sheets with parchment paper.
Whisk All-Purpose Flour (1 3/4 cup), Baking Powder (1 teaspoon), Baking Soda (1/2 teaspoon), and Coarse Kosher Salt (1/2 teaspoon). Set aside.
Using an electric mixer, beat the Powdered Confectioners Sugar (1/2 cup), Dark Brown Sugar (1/2 cup), and Unsalted Butter (6 tablespoon) in a large bowl to blend.
Add the Creamy Peanut Butter (1/2 cup) and beat until creamy. Gradually beat in Vegetable Oil (1/2 cup), Pure Vanilla Extract (1 1/2 teaspoon) then the Large Egg (1).
Add the dry ingredients; mix just until blended. Stir in the Bittersweet Chocolate Chips (1 1/3 cup).
Drop cookie dough by level tablespoonfuls onto the prepared baking sheets, spacing about 1 1/2 inches apart.
Bake cookies until puffed and golden brown, about 10-12 minutes. Cool slightly, then transfer cookies to rack to cool completely.
To make the filling, place Bittersweet Chocolate (3 ounce), Creamy Peanut Butter (1/4 cup), Powdered Confectioners Sugar (2 tablespoon), and Coarse Kosher Salt (1/4 teaspoon) in a medium bowl.
Bring Whipping Cream (6 tablespoon) to boil in a small heavy saucepan. Pour the heated cream over the chocolate mixture; stir continuously until the mixture is melted and smooth.
Chill until the filling is thick and spreadable, about one hour.
Spread about 1 rounded teaspoonful of the chocolate-peanut butter filling on the flat side of one cookie. Top with a second cookie, forming a sandwich. Repeat with remaining filling and cookies.