Position rack in center of oven and preheat oven to 425 degrees F.
Sprinkle beef with salt and pepper. Toss beef with flour in a large bowl to coat. Heat oil in a heavy large casserole or Dutch oven over medium-high heat. Add 1/3 of the beef to the hot oil, and sear until browned on all sides, about 5 minutes. Using a slotted spoon, transfer beef to a clean bowl. Repeat with remaining beef in 2 more batches.
Add beef broth and bring to a simmer, scraping with a wooden spoon to loosen browned bits on bottom. Return all beef and any accumulated juices to pot. Add soup and simmer uncovered, until liquid thickens slightly and beef is tender, about 15 minutes. Divide stew equally among 4 oven-proof mugs.
On a floured surface, cut puff pastry into 4 (4-inch) rounds. Moisten rims of mugs with water. Gently adhere puff pastry to each mug. Transfer to baking sheet and bake until golden brown, about 12 minutes.