Line a baking sheet with parchment paper; set aside.
With clean hands, mix the ground turkey with all of the patty ingredients in a large mixing bowl with. Gently work the mixture until it's cohesive.
Divide the meat mixture into four equal portions and carefully form them into patties. Place the patties onto the parchment-lined baking sheet. With your thumb, press a divot into the middle of each patty; this will prevent the patty from shrinking on the grill.
Place the patties in the fridge and let them chill for about 30 minutes. This helps them firm up so they don't fall apart on the grill.
When it's go time, preheat your grill to medium-high heat—around 450º F. Clean the grill well. If you need to grease your grill, dip a wad of paper towels in some vegetable oil and glide the soaked towel along the grate with tongs. (I don't normally do this, but if you find that meat sticks easily to your grill, you might want to do this step to play it safe; you know your grill best.)
Once the grill is ready, transfer the patties to the grill, cover, and let them cook for about 4-5 minutes. Gently flip them (they should have nicely formed grill marks on the cooked side), cover, and let them cook for another 4-5 minutes. Check the internal temperature with a Meat Thermometer, looking for an internal temperature of 165º F. If you're not quite there yet, flip the burgers once more and cover for another minute or two. (If you're using cheese, place the cheese slices onto the patties about a minute before you think they'll be done.)
When the burgers are ready, transfer them to a clean plate or platter and serve them with fresh brioche buns and your choice of toppings.