Pat the beef cubes dry with paper towels and season them with salt and black pepper.
Heat olive oil in a large heavy-bottomed pot or Dutch oven over medium-high heat.
Add the beef cubes in batches, browning them on all sides for about 5-7 minutes per batch. Remove browned beef and set aside.
In the same pot, add the diced onion and cook for 4 minutes until softened.
Add the minced garlic and cook for 1 minute until fragrant.
Stir in the tomato paste and cook for 2 minutes.
Pour in the red wine, scraping the bottom of the pot to deglaze and loosen browned bits.
Return the browned beef to the pot and add the gluten-free beef broth, dried thyme, dried rosemary, and bay leaves.
Bring the mixture to a boil, then reduce heat to low and cover. Simmer for 1 hour and 45 minutes, stirring occasionally.
Add the carrots, celery, potatoes, and mushrooms to the pot. Cover and continue to simmer for another 45 minutes until the vegetables and beef are tender.
In a small bowl, whisk together the cornstarch and cold water until smooth.
Stir the cornstarch mixture into the stew and cook uncovered for 5-10 minutes until the stew thickens.
Remove bay leaves and adjust seasoning with salt and black pepper to taste.
Serve hot, garnished with chopped fresh parsley.