In a large bowl, combine turkey burger ingredients with 1 Tablespoon of the olive oil until well combined. Form into 5 uniform burger patties and place on a parchment lined sheet pan. Add another sheet of parchment atop and press down gently, lightly flattening patties until uniform.
Preheat a large saute pan or cast iron skillet over medium high heat- for 3 minutes. Add the second tablespoon of olive oil. Add the first batch of patties to the pan- careful not to overcrowd and leave undisturbed another 3 minutes.
Flip and cook an additional 3 minutes, turning down heat as needed. Transfer burgers back to your original sheet pan and transfer to the oven. Bake an additional 5 minutes until just cooked through.
In a small bowl, whisk together greek yogurt with a large drizzle of good olive oil and a sprinkling of salt and pepper.
Begin re-warming the burger saute pan with brown bits over medium heat and add the shallots to the pan. Saute 2-3 minutes until translucent. Stir in peaches, salt and pepper and saute an additional 2 minutes. Off the heat, stir in lemon zest and fresh mint.
To serve burgers, top turkey burger patties with a spoonful of Greek Yogurt Topping spread atop each patty along with a large spoonful of the seared peaches finished with fresh mint and basil leaves.
If serving in buns, I would recommend a buttered brioche roll. Enjoy!