For the cake: Preheat the oven to 350 degrees F. Butter three 8-inch round cake pans and line the bottoms with parchment. Butter the parchment and dust the pans with flour, tapping out the excess.
Whisk together the flour, baking powder and salt in a large bowl. Beat the butter and granulated sugar in a large bowl with an electric mixer on medium-high speed until light and fluffy, about 3 minutes. Reduce the mixer speed to medium and beat in the eggs, one at a time, scraping down the bowl as needed. Beat in the vanilla.
Reduce the speed to medium and add the flour mixture in 3 batches, alternating with the cream, beginning and ending with the flour; beat until just smooth, about 3 minutes.
Divide the batter between 2 of the prepared pans. Bake until the cakes are light golden on top and the centers spring back when pressed, 25 to 30 minutes. Transfer to racks and let cool for 10 minutes. (Leave the oven on for the cookie dough.) Invert the cakes out onto the racks (remove the parchment) to cool completely, about 1 hour. Trim the tops of the cakes with a long serrated knife to make level, if needed.
For the cookie dough: Meanwhile, microwave the flour in a small microwave-safe bowl for 1 minute (see Cook's Note). Remove and stir well. Microwave for an additional minute or until the temperature registers 180 degrees F on an instant-read thermometer. Sift into a medium bowl, then whisk in the baking soda and salt.
Beat the brown sugar, granulated sugar, butter, yogurt and vanilla in a large bowl with an electric mixer on medium-high speed until well combined, about 2 minutes. Add the flour mixture and mix on low speed until well incorporated, about 1 minute. (Turn off the beaters and use your hands to help combine if needed). Fold in the chocolate chips with a rubber spatula or mix them in with your hands. (You should have about 4 cups of cookie dough.)
Remove 1/4 cup cookie dough and roll into 6 heaping teaspoon sized balls and place them 1-inch apart on a baking sheet. Bake until the cookies are set and browned around the edges, 10 to 12 minutes. Cool the cookies on the baking sheet for 5 minutes then transfer to a rack to cool completely, about 25 minutes. Cut the cookies in half.
Make the ganache: Place the chocolate in a medium bowl. Bring the heavy cream to a boil in a small saucepan over medium-high heat. Pour the cream over the chocolate and let sit for 5 minutes. Stir until the chocolate is completely melted and smooth.
Assemble the cake: Place a cake layer on a cake stand or platter. Press half of the remaining cookie dough evenly on top of the cake (it should be about a 1/2-inch-thick layer). Top with the other cake round and then press the remaining cookie dough evenly on top of the cake. Drizzle some of the ganache around the edge of the cake letting it drip down the sides. Drizzle 2 tablespoons of the ganache over the top of the cake. Spread the remaining ganache around the bottom of the cake to make a 1-inch border. Press the mini chocolate chips into the ganache. Decorate the top of the cake with the cookie halves. Chill until the ganache has set, about 20 minutes.
When measuring flour, we spoon into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.) Microwaving the flour to 180 degrees F may reduce the risk of foodborne illness associated with eating it raw or undercooked.
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