In a medium mixing bowl combine the ground chicken, grated garlic, minced sun-dried tomatoes, minced oregano, kosher salt, and black pepper.
Use your hands to gently but thoroughly mix the ingredients until evenly distributed; do not overwork the meat.
Divide the mixture into 4 equal portions and shape each into a patty about 3/4-inch thick.
Heat the olive oil in a 12-inch skillet over medium heat until shimmering.
Add the patties to the skillet and cook until no longer pink in the center and firm to the touch, about 5 minutes per side.
Top each cooked patty with a slice of smoked mozzarella, cover the skillet, and let rest 2 minutes to melt the cheese.
Place each patty on a toasted bun and add microgreens if using, then serve.