For the filling, place 1¼ cups of the milk and the sugar, gelatin, and salt in a large saucepan over medium heat.
Whisk and bring barely to a simmer, whisking to dissolve the sugar and gelatin completely, 2 to 3 minutes.
Meanwhile, in a medium-size bowl, whisk together the egg yolks, cornstarch, and the remaining ¼ cup of milk.
Off the heat, pour 1 cup of the hot milk mixture into the egg mixture and whisk to combine, then strain this mixture back into the saucepan with the remaining hot milk.
Over medium heat, whisk the mixture continuously until it is thickened and bubbling in the center, 4 to 5 minutes.
Remove the pan from the heat and strain the mixture again into a medium-size bowl.
Stir in the butter and vanilla.
Whisk until smooth, then cover with plastic wrap, pressing the wrap directly onto the surface.
Chill the filling for at least 5 hours, preferably overnight.
For the cake, place a rack in the center of the oven, and preheat the oven to 375°F.
Lightly grease and flour the bottoms of two 8″ cake pans.
Sift together the flour, baking powder, and salt in a medium-size bowl.
Set aside.
Place the butter and vanilla in a large mixing bowl, and beat with an electric mixer on low speed until combined, 1 minute.
Slowly add the sugar, beating well on medium-high speed until the mixture is creamy and light, 2 to 3 minutes.
Scrape down the sides of the bowl with a rubber spatula.
Add the eggs, beating in one at a time.
Scrape down the sides of the bowl again.
Alternately add the flour mixture and the milk to the butter and sugar mixture, beginning and ending with the flour.
Beat until smooth.
Divide the batter between the 2 pans.
Place the pans in the oven.
Bake the cakes until they are lightly golden brown and begin to pull away from the sides of the pan, 18 to 22 minutes.
Place the pans on wire racks to cool for 10 minutes.
Run a knife around the edges of the cakes, give them a gentle shake, then invert onto the racks to cool completely, right side up, about 45 minutes.
To assemble the cake, place 1 cake layer on a cake plate.
Spoon the filling onto the center of the cake and spread until it barely reaches the edge of the cake.
Place the second layer on top of the filling.
Place the filled cake in the refrigerator while you make the glaze.
For the glaze, place the chocolate, cream, and corn syrup in a medium-size saucepan over medium-low heat.
Whisk until smooth, 3 to 4 minutes.
When the chocolate has melted, pull the pan from the heat, add the vanilla, and stir until smooth.
Remove the cake from the refrigerator and spoon the glaze over the top of the cake and let it drip down the sides.
Let the cake stand for 10 minutes before slicing.
If not serving the cake immediately, chill it until time to serve.
