Pat beef cubes dry and season with salt and pepper. Toss with flour until lightly coated.
Heat 2 tablespoons olive oil in Dutch oven over medium-high heat. Sear beef in batches until deeply browned, 6-8 minutes per batch. Transfer to plate.
Add remaining oil and butter to pot. Cook onion, carrots, and celery for 5-6 minutes until softened. Add garlic and cook 30 seconds.
Add cremini and porcini mushrooms. Cook 6-8 minutes, stirring occasionally, until mushrooms release liquid and start to brown.
Pour in red wine and scrape up browned bits from pot bottom. Let simmer 2-3 minutes to cook off alcohol.
Stir in beef stock, bouillon paste, and Worcestershire sauce. Return beef and juices to pot. Add thyme and bay leaf.
Bring to a gentle simmer. Cover and reduce heat to low. Braise 1.5-2 hours, stirring occasionally, until beef is fork-tender and gravy thickens.
Remove thyme and bay leaf. Adjust seasoning with salt and pepper. Cool filling at least 20 minutes before assembling pie.
Preheat oven to 400°F. Roll one sheet of puff pastry to fit bottom of pie dish. Press into dish, letting excess hang over edges.
Pour cooled filling into pastry-lined dish and spread evenly. Roll second sheet for top crust. Place over filling, trim excess, and crimp edges to seal.
Cut 2-3 small slits in top crust to vent steam. Brush top crust evenly with beaten egg wash.
Place pie on baking sheet. Bake 30-35 minutes until crust is deep golden brown and puffed. Rest 10 minutes before slicing.