Heat oil in a 5 quart or larger dutch oven over medium-high heat. Add beef and brown for 1 minute per side (4 minutes total). Remove beef from pan and chop into bite-sized pieces.
Add onion and garlic to the pan and sauté for 1 minute. Add a small amount of the beef broth and scrape the brown bits from the bottom of the pan.
Add the carrots, potatoes, thyme and rosemary. Cook for an additional minute until the herbs are fragrant.
Add the remaining broth, beer, mushrooms and tomato paste. Stir to incorporate.
Sprinkle the beef with salt, pepper, cornstarch and flour. Return the beef to the pot.
Bring mixture to a boil; reduce heat, cover and simmer for 45 minutes. Remove from heat and let cool while you assemble the crust.
Preheat the oven to 400°F. While the stew is cooling a bit, cut the puff pastry into two even pieces and roll each lightly with a rolling pin. Sprinkle one half of each piece with blue cheese. Fold the unsprinkled side over the sprinkled side. Lightly roll each piece with a rolling pin again. Place the puff pastry sheets back into the freezer until you are ready to top the pot pies.
Divide the stew mixture between to mini gratin or other small oven-safe pans. Each pan should be able to hold 8 - 10 ounces of liquid. When the oven is heated remove the puff pastry from the freezer and cover each pan with a sheet of puff pastry.
Place pans on a rimmed baking sheet and bake for 35 - 45 minutes, until the puff pastry is golden brown. Remove from oven and cool slightly before serving.