Lightly brush the wells of a muffin pan with butter.
Whisk together the flour and salt in a large bowl. Cut in the butter with a fork, a pastry cutter, 2 butter knives, or your fingertips. It should look crumbly, with some pieces of butter the size of small peas.
Drizzle the water in a little at a time, mixing as you go (you can use a fork to mix, but it works best mixing with your fingertips). Add just enough water so it comes together to form a ball of dough (you may need more or less water).
Divide the dough into 2 equal parts. Roll each into a ball, flatten each ball slightly into a disk, wrap them in plastic wrap, and refrigerate until chilled, about 30 minutes.
Place 1 disk of dough onto a floured work surface. Working from the center out, roll the dough out to a rectangle about 11 to 12 by 16 to 18 inches.
To make the pies in a regular muffin pan, you will need 8 (5-inch) circles to get pressed into the muffin wells, and 8 (3-inch) circles for topping. Stamp out as many as you can, and then repeat this process with the second ball of dough. Gather the dough scraps, re-roll the dough, and stamp out more if needed.
Gently press each 5-inch circle of dough into a muffin well in a muffin pan. If you’re using a standard-sized muffin pan, the dough should come up over the top a little, which is perfect. Use a fork to poke a few holes in the bottom crust of each mini pie.
Fill each muffin well to the top with beef and ale stew (about 3 tablespoons per pie), making sure the filling is compact and there are no air bubbles.
Lightly brush the top ring of dough with eggwash. Place 1 (3-inch) dough circle on top of each pie. Gently crimp the outside with a fork. Lightly brush each dough circle with eggwash, discarding any extra eggwash.
Bake in an oven preheated to 375F until the mini pies are golden, about 35 to 40 minutes.
Let them cool for 15 minutes in the tray before removing (if you run a paring knife along the outside of each mini pie, they should pop right out).
