Make the Pie Crust:

1. In a large bowl, combine the flour and the diced butter. Toss to coat the butter with the flour. Work the butter into the flour using a pastry blender, by using your fingers to squeeze the butter chunks until they're flat and then rubbing them into the flour. Some larger pieces can remain, up to the size of a marble. Continue blending until the dough looks shaggy.
2. Make a well in the center of the flour mixture and add the sour cream to it. Using a spatula, mix 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 dough out until it stretches to the edges of the plastic wrap to ensure a tight seal. Refrigerate for at least 2 hours, but preferably overnight.

Braise the Beef:

1. Preheat the oven to 350°F  and place an oven rack in the middle part of the oven.
2. Heat the oil in a Dutch oven over medium-high heat. Working in batches, brown the meat on all sides. Once browned, remove the beef and set aside.
3. Lower the heat to medium. Add the mushrooms and cook until they are softened and have evaporated all of their liquid, about 8 minutes.
4. Add in the carrots and onions and cook for 8 minutes, until they begin to soften.
5. Add the flour, tomato paste, thyme, garlic, salt, and pepper and cook for 30 seconds until the tomato paste has turned a rusty color. 
6. Deglaze the pot with the beef broth, stout, and sugar, scraping up any browned bits on the bottom of the pot. Nestle the set aside browned beef into the liquid. Bring the mixture up to a boil, cover with a tight-fitting lid, and transfer to the oven. Let braise until the meat is tender and the sauce has thickened, about 1-½ to 2 hours. 
7. When the meat is tender, taste and adjust the seasoning. If too much liquid has reduced and the sauce is salty, add water to balance it out.
8. 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 chill for at least 2 hours or overnight.

Assemble and Bake:

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