Heat the vegetable oil in a large pot or Dutch oven over medium-high heat.
Add the reindeer meat to the pot and cook until browned on all sides, about 5-7 minutes.
Remove the meat from the pot and set aside.
Add the onions, carrots, celery, and garlic to the pot and cook until the vegetables are soft, about 5 minutes.
Add the broth, red wine, tomato paste, bay leaves, thyme, salt, and pepper to the pot and stir well.
Return the reindeer meat to the pot and bring the stew to a boil.
Reduce the heat to low, cover the pot, and let the stew simmer for 1-2 hours or until the meat is tender.
Add the potatoes to the pot and let the stew simmer for another 30 minutes or until the potatoes are cooked through.
Add the frozen peas to the pot and let the stew simmer for another 5 minutes or until the peas are heated through.
Remove the bay leaves from the pot and serve the reindeer stew hot with crusty bread.