Preheat oven to 425F. In a medium bowl, mash together the ground bison, feta, 2 tbsp basil, salt and pepper.
Divide the meat into four sections, roll into a ball, then make into hamburger patties.
Combine mayonnaise, sour cream, Parmesan, shallot, garlic, 3 tbsp basil, 1/4 tsp pepper and salt in a food processor and process until smooth.
Drizzle the tomatoes with olive oil, salt and pepper and bake at 425F until soft (about 10-15 minutes).
Cook the hamburger patties to desired doneness on the grill.
Layer the hamburger bun, burger, sauce, onion slices, cucumber and tomato to serve.