To make the burgers: Gently work together the turkey, mayonnaise, shallot, parsley, Worcestershire and hot sauce. Form into 4 patties.
Film a heavy skillet with the oil and set over high heat. Sear the turkey burgers until they form a crispy, dark crust, about 2 to 3 minutes per side. Reduce the heat to medium and cook through until the meat is no longer pink inside.
To prepare the condiments: Cook the pancetta in a heavy skillet over medium-high, turning often until browned and crisp, about 5 minutes. Drain on paper towels and set aside. Remove all but 1 tablespoon of the fat from the pan and add the sliced mushrooms. Return the pan to medium-low heat, and cook the mushrooms until they begin to release their juices, turning often. Cover the pan for a few minutes, then remove the lid and continue cooking the mushrooms until they are dark and cooked all the way through.
Spread the chèvre evenly over the bottom of each toasted bun. Set the burger on top of the chèvre, then layer the pancetta, the mushrooms and greens onto the burger. Add the top of the bun. Serve right away, passing a little extra mayonnaise on the side.
Nutrition information per serving: