In a large bowl, toss beef with 3 Tbsp flour, 1 tsp salt and 1 tsp black pepper.
In a large pot over medium high heat 1 Tbsp vegetable oil. Add enough beef to pot to form only a single layer (don't overcrowd the pot) brown beef on all sides (takes around 7 mins per batch). Transfer to a large bowl. Brown remaining batches of beef in 2 batches.
Add 1 bottle of ale to pot scraping brown bits with a wooden spoon. Pour ale over reserved beef and return empty pot to med-high heat.
Add remaining Tbsp oil to pot. Add onions and 2 tsp salt, cook stirring often, until onions are transparent and turn a golden color (takes about 20 mins).
Remove lid, raise heat to med-high heat. Stir in 3 Tbsp flour, and cook 3 mins stirring often.
Add mushrooms, reserved beef and ale, remaining bottle of ale, and carrots. Bring to a boil. Cover and lower heat to a gentle simmer. Cook stirring occassionally, until the beef is tender (around 3 hours).
Start to make these about 40 mins before serving-.
In a medium bowl stir together remaining 2 cups of flour, 3/4 tsp salt and 1/2 tsp baking soda.
Using a pastry blender or your fingers work cold butter into flour mixture until it resembles cornmeal with pea sized pieces. In another bowl, whisk together buttermilk and egg.
Gently fold wet ingredients into dry. Mix until a very shaggy dough forms. If more liquid is needed, add additional buttermilk 1 tbsp at a time.
Gently form dough into 12 equal balls and drop into bubbling hot stew. Cover pot and cook 20-30 mins or until the dumplings are fluffy and cooked through.
Let sit 15 minutes before serving. Stew thickens as it cools.