For the Doughnuts:
Preheat the oven to 350°F and lightly grease your doughnut pan if you want to. I do not grease mine, as it is nonstick, and it does not have any issues with sticking.
In a large bowl, add the graham cracker crumbs, flour, salt, baking powder, and baking soda. Whisk together until combined, set aside.
In a medium bowl, add the egg, milk, sugar, oil, and vanilla. Whisk together until entirely combined and then add to the dry ingredients.
Use a rubber spatula to mix the wet ingredients with the dry ingredients until a batter forms. It will be a bit thicker than cake batter, but a bit thinner than brownie batter. Use a spoon and separate the batter amongst the doughnut molds, filling each mold about 1/2 of the way full.
Bake in the preheated oven for 8 minutes. If the tops are still a little squishy, you can bake them for 2 more minutes, but 8 minutes has been perfect for me.
Once you remove them from the oven, allow to cool for 5 minutes, and then remove the doughnuts from the pan. Be careful as the doughnuts and pan will still be hot at this stage, I usually use a butter knife to lift the doughnuts out of the pan. Allow to cool on a cooling rack
For the Frosting:
In a medium sized bowl, add the powdered sugar, strawberry puree, vanilla, salt, and cream. Whisk until combined. This will be thinner than buttercream, but thicker than a normal thin glaze.
Once the doughnuts are cooled, dip the tops into the frosting. Allow to dry and dip one more time for a thicker application.