Heat a large skillet over medium heat and add 1 tablespoon olive oil, chopped celery and onion. Fry until softened about 5 minutes. Add the carrots, garlic, thyme and bay leaves frying for an additional 5 minutes.Stir in the tomato paste and beef broth and pour into a crockpot. Season with salt and pepper.
Add the remaining olive oil to the skillet and fry the elk meat until browned - you may have to do this in batches. Add the meat and chopped parsnips to the crockpot and stir everything together. Cover and cook on high for 4 hours or on low for 6-8 hours.
In a small bowl, dissolve the cornstarch in 2 tablespoons of cold water. Stir the cornstarch mixture into the liquid in the crockpot and cook for 30 minutes until slightly thickened. Season to taste if needed.
Serve over mashed potatoes and garnish with chopped parsley and a pinch of parmesan cheese.