Well, it looks like the busy life of the Mom of a teen means I only post when it is SERIOUS - and, friends, if you've been here before, you know there is nothing I take more seriously than Pi day pies!
This year's pie is a "raised pie" - a British-style pie made to stand on its own without a pie plate. Conveniently, raised pies are in the shape of a cylander, so this year we're using that calculation in our decorations.
Math first! Imagine you unfold and flatten out your cylinder - the surface area of a cylinder is the area of the top and bottom circles, so πr^2 + πr^2, plus the dimensions of the rectangle that wraps around them, which is π(diameter)(height) All together, the equation is 2πr^2 + πDH. More about that later.
Our pie today was chosen partly because it's cylindrical, but mostly because it's delicious: it is a traditional hearty meal in Shropshire, a county mostly to the east of Wales, whose tourism site claims the recipe is over 400 years old. Made with "gammon" (a kind of ham,) apples, cider, potatoes, onions and sage, it's kind of like a delicious meatloaf in a crust. Its name is possibly for an ancient word for apples, or an old word for a six-sided shape - no one really seems to know, but it wouldn't be British if it didn't have a quirky name.
We of course took liberties with the recipe - cream instead of cheese, pork and bacon instead of ham - we love it as a meal-in-one with a nice salad (arugula, if you want a particularly British meal.)
Whisk together the flour and salt in the bowl of your mixer, with the dough hook attached. Combine the butter, shortening, milk and water in a saucepan and bring to a boil. Slowly pour the contents of the saucepan over your flour, mixing slowly after each addition, and then scrape your bowl to make sure all the flour is combined. Knead with the dough hook until you have a smooth and elastic dough. Set aside in a warm place.
Preheat your oven to 360 degrees (or 375 if your oven isn't circle-friendly.) and butter a 9" springform pan (springform is critical)
Fidget pie filling ingredients
2 medium potatoes (I used 4 small)
2 cups of ground pork (I used a combination of ground and diced)
1/4 lb of bacon, diced
4 large sage leaves, finely chopped
Half a 12 oz bottle of hard cider
1/4 tsp ground mace
1 tablespoon brown sugar
2 large apples
1 tsp salt
1 egg for glaze
about 1/3 cup whipping cream to finish
Pour the cider into a large bowl. Peel and dice the apples and potatoes and onions and toss them in. Add the remaining ingredients except the egg and cream, and mix with your hands until well combined.
Divide your pastry dough in quarters; remove one and set aside. Roll out the remaining 3/4 dough into a large circle about 3" bigger around than the circumference of your springform pan. Carefully fold the pie dough into quarters, drape it inside the prepared pan and open it, making sure it is pushed carefully into the corner all the way around the bottom. Drape the excess over the outside of the top of the pan.
Pour in the filling (do not pack it, just spread it in gently.)
Roll out the remaining dough to a circle about an inch and a half bigger than the springform pan. (See below for pi day decoration method.) Drape it over the filling, with the excess overlapping the edges of the inside dough. Pinch the top and bottom crust together firmly and trim to about 1" outside the edge of the springform pan. Pull the pinched dough straight upright and fold it double. Crimp the pie by pinching the dough and folding down the excess, continuing all the way around the pie (or you can just flute it, if it's pinched very well.) Make sure there are vent holes in the crust, then whisk the egg thoroughly and glaze the top of the pie with the egg.
Put the pie on a baking sheet and pop it into the oven for 1 hour. Turn off the oven after an hour, and allow the pie to sit in the cooling oven for 1/2 hour. After the pie has come out of the oven, use a knife to loosen the filling in the vents, and pour in 1/3 cup of whipping cream. Serve.
To make the decoration, fold your top crust into quarters so you have guide lines. Decide how tall your cylinder will be, and mark that height in the center of one of the two guide lines. Using a large bottle cap, cut out two circles bisecting the guide lines on either side of the mark. Roll out the dough scraps, and cut a long strip of pastry whose width equals your cylinder's height. Using the bottle cap, roll the edge along the side of the dough the full circumference of the cap, creating an indentation that gives you the length of your cylinder (do the same for the other side of the strip.) Measure the diameter of your bottle cap, and mark that length with an indentation - the remainder is π for this cylinder.