Preheat oven to 350. Butter and flour lightly 3- 9"cake pans and line with either wax paper or parchment. You can use two (which I did in the image) and you'll just bake the cake a little longer. Pour the milk and vanilla into a glass measuring cup.
Combine the flours and place in a medium bowl.
Divide the batter evenly among the pans. Three pans: Bake for 20-25 minutes. Two pans: Bake for 25-30 minutes. Either way, check with a cake tester which should be clean.
Combine the milk and sugar in a medium saucepan. Whisk in the flour and bring to a boil over medium heat, whisking the whole time until thick and bubbly, which should take about 5 minutes.
Remove from heat and add coconut. Stir in vanilla, cover and set aside to cool completely.
Get ready by putting the egg whites and vanilla in a large mixing bowl of electric mixer.
Place one layer of cake on your serving platter or cake plate and spread 1/2 of the filling on top. If you're only using two layers, use as much as makes sense to you and save the rest to eat vanilla wafers or graham crackers and chocolate for an upscale s'more.
Place the next layer on (and repeat steps 1 & 2 if necessary).
Frost the top and sides of the cake with the frosting.