Generously season beef pieces with salt and fresh cracked black pepper. Add olive oil to a hot Dutch oven or large pot. Brown the beef pieces on all sides in small batches. When browned, remove with a slotted spoon and set aside on plate.
Add diced onions to the same pot and sauté for 2–3 minutes until they are translucent. Add garlic and cook for 1 minute. Next, add the tomato paste, Worcestershire sauce, thyme, Italian seasoning, bay leaves, and brown sugar. Stir until incorporated. Add the beef back into the pot along with the juices.
Pour in the Guinness stout and beef stock. Turn heat up to medium-high heat, and bring the stew to a boil, about 5 minutes.
In a small bowl, combine flour and 3 tablespoons beef stock and mix until smooth. Add to boiling stew and stir well. Add potatoes and carrots. Turn the heat down, cover and simmer on low for an hour, stirring often. Add peas the last 15 minutes of cooking. Add salt and fresh cracked black pepper to taste.
Preheat oven to 400°F. Roll out puff pastry on a clean counter top to remove creases. Using standard ramekins (or any individual baking dishes you have on hand), place face down onto puff pastry and gently cut around dish using a sharp knife.
Ladle each ramekin with prepared stew and top with cut puff pastry. Stretch and press the pastry gently around the edges of the ramekin to prevent shrinkage while cooking.
In a small bowl lightly beat egg white and water. Brush puff pastry with egg mixture using a pastry brush. Using a knife, cut a slit in the middle of each pot pie.
Place prepared ramekins on a cookie sheet and bake in 400°F oven for 20-25 minutes or until puff pastry is lightly golden brown and beef mixture is bubbly. Let sit for 10 minutes before serving.