Start by melting butter in a pan over low heat. Roughly chop your mushrooms and toss them in the butter. Place a lid on pan and cook the mushrooms for 3-4 minutes to brown them.
Stir chopped walnuts into the pan. Return the lid to the pan and heat for another 2-3 minutes, until you can smell the walnuts become toasted in the butter.
Take the ingredients off the stove. Combine them in a food processor with the garlic and green onion. Pulse until you have a creamy blend and set aside to cool.
In a mixing bowl, combine the ground turkey, salt, pepper, thyme, rosemary, oregano, parsley, and paprika. Form the mixture into 2 portions and flatten on a clean surface.
Place an equal portion of stuffing in the center of each flattened turkey patty. Fold the turkey over the stuffing to form a ball. Turn the ball over so the seam is on your surface and press down slightly to seal the burger patty.
Heat the olive oil in a pan over medium heat. Place the patties in the oil, seam side down, and flatten down with a spatula. Place a lid over the pan and cook the burgers for 4-5 minutes per side. Adjust the heat as necessary to avoid burning.
Let the burgers cool off the stove before adding any toppings.