Preheat oven to 350 degrees F. Position racks in the upper and lower thirds of the oven. Coat 2 large baking sheets with cooking spray.

To prepare cookies: Beat oil, brown sugar, egg and vanilla in a large bowl with an electric mixer on medium speed until combined. Whisk flour, cocoa, baking powder, baking soda and salt in a medium bowl. Gradually add the dry ingredients to the wet ingredients, alternating with milk; beat until smooth. Let the batter stand for 15 minutes.

Drop batter by the tablespoonful onto the prepared baking sheets, spreading the batter into a 2- to 3-inch circle with the back of a spoon if it doesn't spread itself. (Each large baking sheet accommodates 8 cookies; they will be close together.) Bake the cookies until firm to the touch, about 8 minutes. Let cool on the baking sheet for 2 minutes, then transfer to a wire rack to cool completely. Wash, dry and coat the baking sheets with cooking spray again. Repeat with the remaining batter.

To prepare filling: While the cookies cool, stir water and gelatin in a small heatproof cup or bowl. Let stand 1 minute. Microwave, uncovered, on High until the gelatin has completely dissolved but the liquid is not boiling, 20 to 30 seconds. (Alternatively, bring 1/2 inch water to a gentle simmer in a small skillet. Set the bowl with the gelatin mixture in the simmering water until the gelatin has dissolved completely.) Stir the mixture until smooth. Let cool for 10 minutes.

Beat cream, yogurt, confectioners' sugar and vanilla in a medium bowl with an electric mixer on high speed until very thick, about 1 minute. With the mixer beating constantly, add the gelatin mixture in a steady steam until well combined. Cover and refrigerate until the cream filling is thickened to the consistency of pudding, about 30 minutes. Whisk again until smooth.

To assemble whoopie pies: Turn half the cookies bottom side up and top with a generous 2 tablespoons of the cream. Top with the remaining cookies. Chill in the refrigerator until the filling is set, about 30 minutes.

MAKE AHEAD TIP: Press a piece of plastic wrap directly on the surface of the filling (Steps 4-5) and refrigerate for up to 1 day. Store the cookies (Step 3) in an airtight container at room temperature for up to 1 day. Refrigerate the assembled Whoopie Pies, uncovered, for up to 4 hours.