Bake the Cake Layers: Start by heating your oven to 350°F. Grease and line two round cake pans. In a bowl, mix flour, baking powder, and salt. In another bowl, beat butter and sugar until light and fluffy. Add eggs one at a time, then stir in vanilla. Alternate adding dry ingredients and milk until the batter looks smooth. Divide evenly and bake for about 25 minutes until the tops spring back.
Make the Vanilla Cream: Pour milk into a saucepan and warm it over medium heat until steaming. In a bowl, whisk sugar, cornstarch, and egg yolks until smooth. Slowly add warm milk while whisking. Return everything to the pan and cook while stirring until thick. Remove from heat, then mix in butter and vanilla. Cover and chill until fully cool.
Prepare the Chocolate Glaze: Heat heavy cream in a small saucepan until it starts to steam. Pour it over chocolate chips and butter in a bowl. Let it sit for a minute, then stir until glossy and smooth. Set aside to cool slightly so it pours nicely.
Assemble the Cake: Place one cake layer on a plate. Spread the chilled cream evenly on top. Set the second cake layer gently over the filling. Slowly pour the chocolate glaze over the center and guide it toward the edges with a spoon. Let it set before slicing.
