Heat a large pot or Dutch oven over medium-high heat. Add the olive oil and heat until it starts to lightly smoke. Add the ground venison and season with salt and pepper. Using a wooden spoon, break up the meat into small pieces. Cook until it is golden brown, around 3 to 5 minutes.
Lower the heat to medium. Add the onions, garlic, thyme, and oregano. Cook until the onions just begin to soften, around 5 minutes. Add the tomato paste and stir to combine. Add the chicken stock, diced tomatoes, tomato sauce, paprika, and Worcestershire sauce. Season to taste with salt and pepper. Bring to a slow simmer and cook for around 20 minutes to slightly thicken and to develop the flavors.
Meanwhile, cook your pasta according to the directions on the package in a large pot of salted water. Once al dente, drain the pasta.
Add the drained pasta to the venison and tomato mixture. Slowly simmer until slightly thickened, around 5 minutes. If the sauce is too thick, thin it out with a little chicken stock. Stir in the fresh parsley and shredded cheddar cheese.
To Serve
Serve in bowls topped with chopped fresh parsley and more shredded cheddar cheese.
NOTES
Brown the venison well. Cook the ground venison until it is golden brown, not just gray. That first browning step builds a lot of the flavor in the finished sauce.
Cook pasta separately. Boil the pasta in salted water until al dente, then add it to the sauce at the end. This keeps the pasta from soaking up too much liquid and helps the sauce stay richer.
Keep simmer time short. After adding the tomatoes, sauce, and stock, simmer for about 20 minutes, then only a few more minutes after the pasta goes in. Ground venison is lean, so longer cooking can make it eat drier.
Loosen before serving. If the goulash gets too thick after the pasta goes in or during reheating, add a small splash of chicken stock to bring it back.
Make ahead if needed. This reheats well, so it is a good dish to make ahead. Let it cool, then store it in an airtight container for up to 4 days.
Freeze for best texture. If you plan to freeze it, freeze the sauce and pasta separately when possible, then thaw overnight in the refrigerator and reheat gently.