In a small jar, combine cornstarch and water. Seal jar and shake vigorously. Set aside.
Pat beef dry with paper towels and season with salt and pepper.
In a large Dutch oven, heat oil over medium-high heat until shimmering. Working in batches, add beef in a single layer to pan and cook up to 1 minute on each side until well browned. Transfer beef to a plate and repeat until all meat is browned. Reduce heat to medium.
Add onion, garlic, celery, and carrots to pan and cook, stirring, until soft and slightly browned, about 5 minutes.
Add beer, stir to scrape browned bits from bottom of pot, and continue to cook over medium heat until most liquid has evaporated, 15 to 20 minutes. Add stock and cornstarch mixture and bring to a simmer. Add beef, mustard, and bay leaf, reduce heat to medium-low, and cook, partially covered, about 2 hours, or until beef is tender. Turn off heat and discard bay leaf.
Heat oven to 375°F. In a medium skillet, melt butter over medium heat. Add mushrooms and cook, stirring, until soft and evenly browned, about 7 to 8 minutes. Remove from heat.
While beef cooks, unfold puff pastry into a single layer on a floured surface and roll into a 14-inch-long rectangle. Invert a mini soufflé dish on top, and, using the tip of a paring knife, trace a circle about ½ an inch wider than the dish’s edge. Repeat to create 4 pastry circles and refrigerate until ready to assemble pies.
Add mushrooms and peas to Dutch oven, stirring to distribute. Gently fold in blue cheese.
Divide beef filling equally between 4 soufflé pans. Brush rims of each dish with egg. Top each with a puff pastry round and crimp along edges of dish to seal crust. Poke a small hole in the center of each pie to vent steam. Bake 35 to 40 minutes, until pastry is golden brown. Remove and let cool at least 10 minutes before serving.