Heat a large skillet over medium-high heat. Add the avocado oil or olive oil.
Pat the deer roast dry with a paper towel. Season all sides with black pepper.
Once the skillet is very hot, add the deer roast. Quickly sear for 15–20 seconds on each side, including the edges, using tongs to turn the roast. The goal is simply to brown the outside.
Place the browned deer roast in the bottom of a large crockpot.
In a medium bowl, combine the water, ranch dressing mix, brown gravy mix, and zesty Italian dressing mix. Stir until well combined.
Pour the seasoning mixture over the deer roast.
Cover and cook on LOW for 7 hours. Do not open the lid or flip the roast while cooking.
When the roast is almost fully cooked, whisk together the cold water and cornstarch in a small bowl.
Pour the cornstarch mixture into the liquid around the roast and gently stir.
Turn the crockpot to HIGH and cook for an additional 30 minutes, or until the gravy has thickened.
Shred the deer roast directly in the crockpot and stir the meat into the gravy.
Serve warm with mashed potatoes, fresh vegetables, or your favorite side dishes.