First, season the goose legs and thighswith kosher salt and black peppergenerously on all sides.
Add oil to the pressure cooker pot and set to the brown or sauté setting. Sear the goose legs and thighs for about 2 to 3 minutes per side.
Add broth, and 2 teaspoons each of the onion powder, garlic powder, and dried oregano. Set the pressure cook setting on high. Cover, lock the lid, and cook for 30 minutes.
Once it is finished cooking, don't touch it right away! Keep the lid closed and locked and allow for 15 - 25 minutes of natural pressure release. This extra time is important because it allows the pressure cooker to continue to work its magic on the tough birds before you open it up to shred the meat.
Open the lid carefully and transfer the meat to a large plate and shred with tongs or two forks. Discard the bones.
Add the red wine vinegar, ½ teaspoon each of garlic powder, oregano, paprika, cumin. Toss well to combine and set aside.
Top with cooked and shredded goose meat, feta, and mozzarella cheese. Sprinkle the nachos evenly with the remaining ½ teaspoon each of garlic powder, onion powder, and dried oregano. Place in the oven and bake at 400 degrees F until mozzarella cheese is melted, about 5 minutes.
Remove from the oven and top with onion, olives, tomatoes, and lettuce. Serve immediately with the tzatziki sauce.