Combine the diced tomatoes, cucumber and red onion with the chopped fresh parsley. Add a pinch of kosher salt and the red wine vinegar. Toss well to combine and set aside.
In a food processor or bowl, combine the cream cheese and feta. Process or whip with a hand mixer until smooth.
Add parsley, oregano, mint, garlic, walnuts ½ teaspoon salt, black pepper and olive oil in your food processor. Process until it resembles a loose pesto.
Place ground turkey in a bowl and add the herb/walnut mixture. Combine until just incorporated.
Form four ½ inch thick patties and set aside.
Heat your grill or grill pan over medium-high heat. Brush the insides of your burger buns with a little olive oil, and grill for 4-5 minutes until toasty.
Lightly season the top of your burgers, then add to the grill salted side down. Salt the other side of the burgers in the pan. The meat is already seasoned, so the outside needs just a touch, but it makes a huge difference!
Grill for 5-6 minutes, until the underside has grill marks and the sides look cooked. Flip over.
Add a spoonful of the whipped feta mixture to the top of each burger and spread it out a bit. Cook the burgers for 3-4 more minutes, until a meat thermometer inserted into the middle reads 160 degrees Fahrenheit and the feta mixture is a little melty.
Place each burger on a burger bun, and, using a slotted spoon, top with the tomato-cucumber mixture, then the arugula. Finish off with a crank of pepper and the top of the bun. Serve with sweet potato fries and a simple side salad.