Preheat the oven to 375 degrees F. Place garlic cloves in a baking dish and drizzle olive oil over cloves. Roast in oven for about 10 minutes, or until fragrant.
Heat a teaspoon of olive oil in large frying pan over medium high heat. Add spinach to pan and toss frequently until wilted, about 4-5 minutes. Use the tongs to gently transfer the spinach to a colander. Squeeze the water out of the spinach and let it rest until room-temperature.
Roughly chop the wilted spinach and garlic so that you can more easily mix them in with the ground chicken. Add it to a mixing bowl with the chicken, feta, Dijon mustard, hot sauce, salt, and pepper.
Gently, but thoroughly, mix everything together until all of the ingredients are evenly distributed. Form into 5 burger patties that are at least ¾ of an inch thick.**
Preheat grill to medium-high. Soak a wadded paper towel generously with olive oil and use tongs to rub it over the clean grill grates, heavily oiling them. Ease the burger patties onto the grill and do not move them for 5-6 minutes. Flip the burgers and let them continue to cook for another 5-6 minutes, or until the burgers release from the grill and the interior temperature of the thickest part of the burgers reaches 165°F. Transfer the burgers to a clean plate.
Serve the burgers on a bun, salad or lettuce wrap. Garnish and serve!