Season liver with ¼ tsp (1 mL) salt. Season stewing beef with remaining salt and pepper. Heat 1 tbsp (15 mL) oil in small Dutch oven (2.5 L) set over medium-high heat. Cook liver 4 to 5 min. until browned. Transfer to plate. Cool completely, cover and refrigerate until needed.
Meanwhile, heat remaining oil in same Dutch oven. Brown stewing beef in batches, 8 to 10 min. per batch. Transfer to plate. Reduce heat to medium. Add onion, carrots, celery, garlic, thyme and rosemary to Dutch oven; cook 5 min. until softened. Sprinkle on flour; cook, stirring, 2 min. Stir in tomato paste; cook 1 min.
Slowly stir in beer and broth; bring to a boil. Return stew beef to Dutch oven. Reduce heat to medium-low. Simmer, partially covered, stirring occasionally, 1½ to 2 hr., or until beef is tender and sauce is thickened. Stir in peas and liver (and any accumulated juices).
Meanwhile, preheat oven to 400˚F (200˚C). Drape puff pastry over Dutch oven (sides of pastry will overhang). Beat egg with 1 tbsp (15 mL) water; brush over pastry. Cut three steam vents on top. Bake 25 to 30 min. until pastry is golden brown and filling is bubbling.
Pie filling can be prepared one day in advance. Liver can be substituted with mushrooms. Lighten up the filling by replacing up to 1 lb (500 g) stewing beef with quartered cremini mushrooms.