Cook the bacon. In a large Dutch oven or heavy stockpot, cook the bacon over medium heat until crisp. Transfer the bacon to a paper towel-lined plate with a slotted spoon, leaving the drippings in the pot.
Brown the beef. Working in batches, brown the beef in the bacon drippings over medium-high heat, adding canola oil if needed to prevent sticking. Sprinkle each batch with salt and pepper. Transfer the browned beef to a plate and keep any juices that collect.
Cook the vegetables. Add the leeks, carrots, celery, onion, and mushrooms to the pot and cook until the vegetables begin to soften, about 6 minutes. Add the garlic and cook for 1 minute.
Add the tomato paste. Stir the tomato paste into the vegetables and cook until evenly incorporated.
Build the stew. Add the beef broth, stout, bay leaves, thyme, and rosemary. Return the beef, its juices, and the bacon to the pot and bring the mixture to a boil.
Simmer the beef. Reduce the heat to low, cover, and simmer for about 90 minutes, or until the beef is tender.
Add the potatoes. Stir in the potatoes, cover, and continue simmering for about 15 minutes, or until the potatoes are tender.
Thicken the stew. In a small bowl, whisk the cornstarch and cold water until smooth. Stir the slurry into the stew, bring it to a simmer, and cook for about 2 minutes, stirring, until thickened.
Add the peas. Stir in the frozen peas and cook until heated through, about 2 to 3 minutes.
Finish the stew. Remove and discard the bay leaves and thyme stems. Taste and adjust the seasoning before serving.