Make the Cake: 1. Position a rack in the lower third of the oven and preheat the oven to 325 degrees F. Grease and flour a 12-cup Bundt pan.
In a large bowl, sift together the flour, baking powder and salt.
Using an electric mixer, beat the butter and vanilla on medium speed until smooth and creamy. Add the sugar and beat until evenly mixed, about 1 minute. With the machine still running, slowly pour in the oil and beat until light and fluffy, about 2 minutes. Add the eggs and egg yolks, one at a time, beating thoroughly after each addition.
Reduce the mixer speed to low. Alternately mix in the flour mixture and buttermilk in 3 additions each, ending with the buttermilk. Mix on low speed just until the batter is smooth and no lumps remain. Turn off the mixer and gently fold the batter several times by hand with a spatula to ensure everything is incorporated. Pour the batter into the prepared pan.
Bake until a cake tester inserted into the center comes out clean, 60 to 70 minutes. Place the pan on a wire rack and let cool completely in the pan, about 2 hours.
Make the Cream Filling: Using an electric mixer on medium speed, beat together the marshmallow crème, butter, and vanilla until smooth. Transfer to a pastry bag fitted with a large round tip or spoon it into a large resealable plastic bag with a bottom corner snipped off.
Fill and Assemble the Cake: While the cake is still in the pan, use a paring knife or an apple corer to make 6 or 7 deep, evenly spaced holes in the bottom of the cake, each about ¾ of an inch in diameter, being careful to cut no more than halfway through to the top of the cake. Discard (or eat!) any cake scraps. Using your fingertips, gently forge a horizontal tunnel through the cake that connects the vertical holes.
Insert the tip of the pastry or plastic bag into each hole and squeeze in some of the filling, tilting the bag back and forth as you work to encourage the filling to make its way into the horizontal tunnel. When the cake is filled, use a spatula to scrape away any excess filling from the bottom of the cake.
Quickly and carefully turn the cake onto a platter. Dust with powdered sugar and serve. Leftovers can be stored in an airtight container (or covered tightly with plastic wrap) at room temperature for up to 4 days.