Bake for approximately 35 minutes, until the top springs back when lightly pressed and a toothpick inserted into the center comes out clean.
For the next step, and for the splitting, wax paper is your friend. Any surface that carries a cake layer, I line with wax paper for easier transfer.
Allow the cakes to cool in their pans on a cooling rack for at least an hour. When completely cool, run a knife around the sides to release the cakes, cover each pan with a wax paper-lined plate, and flip. Gently lift the pans off of the cakes, and carefully peel back the pieces of parchment, taking care not to take the very tops of the cake with you. (I did end up pulling off a teeny tiny bit of the top of one layer, but it didn't matter, since the cake would ultimately be covered in whipped cream.)
Wrap the two cakes in plastic wrap, and refrigerate at least three hours, or overnight.
Meanwhile, prepare the strawberries:
Slice the strawberries thinly (but not too thinly - you want the slices thick enough so that you can really taste and feel the berries even once they are smothered by custard, cake, and whipped cream!), and place in a bowl. Sprinkle with the 2T. sugar, and stir. Allow the strawberries to macerate for 1 hour. Their juices will release and pool at the bottom of the bowl. Every so often, give them a stir. Strain the berries, reserving the released juices.
When the cakes are thoroughly chilled, and thus a little sturdier, it's time to split them in two. Using a long serrated bread knife, carefully saw each layer in half. Place each layer on a wax paper-lined baking sheet or plate.