Preheat oven to 375 degrees.
Begin by preparing mashed potatoes. Peel and cube potatoes and then place them into a pot with cold water. Bring them to a boil and then boil for 10 minutes, or until fork tender. Drain and add cream, 2 tbsp. butter, and salt. Once butter melts, mash until smooth. Set to the side.
In a large skillet or dutch oven, melt 1 tbsp. butter over medium heat. Add ground venison and brown until cooked through, breaking it up as you go. Transfer to a plate to the side.
To skillet, add remaining 2 tbsp. of butter and melt. Add diced onions, carrots, and celery and saute until onions are translucent, around 3-4 minutes.
Add garlic and quartered mushrooms saute until the mushrooms release their liquid, about 5 minutes. Add peas and tomato paste and stir to coat, cook for 2 minutes.
Add flour and stir to combine. Cook for 2 minutes.
Reduce heat and slowly add in herbs and broth, stirring constantly. Once fully combined, sauce should resemble a thick gravy. Stir in cooked venison. Turn off heat.
If using cast iron or a dutch oven, you can use the same dish to bake in. Otherwise, transfer mixture to a casserole dish.
Top with prepared mashed potatoes and shredded cheese.
Bake for 20-25 minutes until the top starts to turn a light brown.