As a note, I like to have all of my beer bread ingredients measured out before starting. While the vegetables are softening, I will mix together the biscuit batter. Instructions for mixing the batter are at the end of the recipe.
Preheat the oven to 350 degrees F. Make sure the beef is cut into small chunks – around 1 inch in size, so the beef can cook through in the oven. Season the beef with salt and pepper. Sprinkle with the flour and toss well to evenly cover the beef.
Heat a 5 quart enamel skillet/pot (or a large cast iron) over medium high heat. Add the oil and once it’s shimmering, add the beef in a single layer. You might have to do 1 to 2 batches. Sear the beef on both sides until it is golden brown, about 2 to 3 minutes per side. Remove the beef with a slotted spoon and set it aside on a plate.
Keep the heat until the skillet on medium-low. Add in the butter. Once melted, stir in the onion, carrots, celery and garlic with a pinch of salt and pepper. Stir in the thyme. Cook until softened, about 5 to 6 minutes. Use a wooden spoon to stir the vegetables and help scrape any brown bits of flavor from the bottom of the pot.
Stir in the mushrooms. Let them cook for about 5 minutes, until they soften. Stir in the tomato paste and cook for another 5 minutes.
With the heat on medium, stir in the Guinness and scrape the bottom of the pan again. Add the beef back to the skillet along with the beef stock. Bring the mixture to a boil then turn off the heat. Stir in peas.
Spoon the beer bread batter (directions below) on top of the pot pie in ½ cup biscuit-like drops. Drizzle the melted butter over top of the batter.
Bake the pot pie for 65 to 75 minutes, or until the bread is golden brown and set on the bottom. Be sure to gently check under the biscuits and see if the dough is cooked through.
Remove from the oven and let the pot pie cool slightly before serving.