Season the beef chuck with salt and black pepper, then toss it with the all-purpose flour until evenly coated. Heat the vegetable oil in a Dutch oven over high heat until shimmering, and the beef should look dry-coated and floury before browning.

Brown the beef in batches in the hot oil, turning to sear on multiple sides. Cook until deep golden-brown with a crust, then transfer to a plate before adding the next batch.

Reduce heat to medium and add the chopped red onion to the pot, cooking for 5 minutes until softened. The onion should turn translucent around the edges.

Add the minced garlic and tomato paste and cook for 1 minute, stirring constantly to prevent scorching. The mixture should become fragrant and slightly darker.

Pour in the stout and scrape the bottom of the pot to release browned bits. Simmer for about 1 minute until you see the liquid darken and loosen the fond.

Add the beef broth, balsamic vinegar, smoked paprika, and dried thyme, then return the browned beef to the pot. Stir to combine so the seasonings disperse evenly and the stew looks richly colored.

Cover the Dutch oven and bring to a simmer, then simmer for 2 hours. Keep a steady gentle bubble—small bursts across the surface—so the beef turns very tender.

Add the cubed purple potatoes and sliced carrot rounds, then simmer for 45 minutes. The potatoes should yield easily with a fork and the stew should thicken slightly.

Stir in the drained black beans and simmer for 10 minutes. You should see the beans warm through and the stew become cohesive without boiling hard.

Bake the puff pastry bat shapes at 400F until golden. Look for puffed layers and browned edges for a crisp topper.

Ladle the stew into bowls and float one puff pastry bat on each serving. The bat should sit on top without sinking, creating a noticeable golden silhouette over the dark stew.