Make the Pie Crust:

1. Add the flour into a large bowl. Add in the diced butter and toss to coat with the flour. Work the butter in the flour using a pastry blender. Or, using your fingers by squeezing the butter chunks until they're flat and then rub the butter into the flour. Some larger pieces can remain, up to the size of a marble. Continue this until the dough looks shaggy.
2. Make a well in the center of the flour mixture, and add in the sour cream. Using a spatula combine the sour cream in the flour.
3. Using your hands, knead the dough a few times to help blend the sour cream into the flour, until it just comes together as one large ball.
4. Transfer the pastry to a work surface, and shape into a rough disk shape. Place the dough in a piece of plastic wrap and wrap tightly. Using a rolling pin, roll the wrapped dough out until it stretches to the corner of the plastic wrap. Refrigerate for at least 2 hours, but preferably overnight.

Braise the Beef:

1. Place oven rack in the middle and pre-heat oven to 350ºF.
2. Heat oil in a dutch oven over medium-high heat. In batches, brown meat on all sides. Once done, remove the beef and set it aside.
3. Lower the heat to medium. Add the mushrooms and cook over medium heat until they are softened and have evaporated all of its's liquid, about 8 minutes.
4. Add in the onions and carrots and cook for 8 minutes, until they begin to soften.
5. Add the garlic, flour, tomato paste, thyme and cook for 30 seconds until the red paste has turned a rusty color. Deglaze the pot with beef broth, stout, and sugar. Return the meat back to the pot. Bring the mixture up to a boil, cover with a tight-fitting lid and transfer to the oven and let braise until the meat is tender and the sauce has thickened, about 1-½ to 2 hours. When the meat is tender, taste and adjust the seasoning, adding salt if necessary. If too much liquid has been reduced, and the sauce is salty, add water to balance it out.
6. Transfer the braised beef filling to a shallow container and let cool at room temperature until no longer hot, about 1 hour. Transfer to the refrigerator and let cool, at least 2 hours or overnight in the refrigerator.

Assemble and Bake:

1. Preheat the oven to 400ºF. Place 6 (8-ounce) ramekins on a sheet pan. Roll out the pastry thin and cut circles to fit over the top of the ramekins.
2. Divide the filling between the ramekins and place the pastry circles on the top. Brush the pie with egg wash and cut a slit in the crust to allow the steam to vent.
3. Bake the pies in the lowest rack until the crust is golden brown, about 30-35 minutes. Let cool for 5-10 minutes before serving.