In a large bowl, mix venison, ¾ teaspoon kosher salt, and ¼ teaspoon each black pepper, onion powder, garlic powder, thyme, and 1 tablespoon oil with your hands until well combined. Form into four 6-ounce patties, about ½ inch thick.
Preheat the oven to 425 degrees F and set the rack in the center of the oven. Line a rimmed baking sheet with parchment paper. Using only ⅓ of the baking sheet, evenly sprinkle 1 tablespoon of the oil with ⅛ teaspoon each salt, pepper, garlic powder, and ground thyme. Place the potatoes over the seasoning, cut side down in an even layer. Sprinkle the tops with a pinch more salt. Bake for 10 minutes while you season the meat and slice the onion and mushrooms.
Scatter sliced onion, sliced mushrooms, and whole garlic over the remaining ⅔ of the baking sheet and sprinkle with salt and pepper. Place in the oven and roast for 10 minutes.
Remove from oven and nestle hamburger steaks onto the pan with ½ tablespoon of butter on top of each and return to the oven and bake for 10 more minutes.
Take pan out of the oven. Preheat oven to broil setting. Meanwhile, use tongs to flip potatoes to cut side up. Transfer half of the onions and mushrooms and any accumulated juices on the pan to a blender. Return pan to the oven and broil for 5 minutes until the hamburger steaks reach an internal temperature of 130 degrees F.
Meanwhile, to the blender add beef broth, soy sauce, and heavy cream. Blend for about 30 seconds until you end up with a smooth gravy. Season with more salt and pepper if necessary.
Remove pan from oven. Transfer steaks to platter. Scatter remaining mushrooms and onions over steaks. Pour two tablespoons of the gravy over each steak. Serve remaining gravy on the side with crispy roasted baby potatoes.