For the sauce, mix together all ingredients in a medium bowl. Cover and refrigerate until serving (or up to 2 days).
For the burgers, heat the oil in a large skillet over medium heat. Add the spinach and garlic, and cook, stirring constantly, until the spinach is wilted, about 2 to 3 minutes. Remove from the heat and cool.
Add the turkey, cooled spinach, and all remaining burger ingredients to a large bowl and use your hands to gently combine, being careful not to over-mix.
Shape the burgers into 6 or 8 patties, depending how big you want them, and chill in the fridge for an hour (or up to 4 hours). Let the burgers sit at room temperature for 10 minutes right before you cook them.
You can cook these over medium-high heat (about 5 to 7 minutes per side) on an oiled grill or grill pan, but I love using my cast iron skillet on the stovetop because they take on a gorgeous golden color.
Serve the burgers along with the Tzatziki Sauce and any toppings you like.