In a large bowl, combine the ground turkey, finely chopped spinach, feta cheese, minced garlic, seasoned bread crumbs, Worcestershire sauce, black pepper, and olive oil. Mix gently until everything is evenly incorporated, being careful not to overmix.
Divide the mixture into 4 equal portions. Shape each portion into a patty approximately 4 inches wide and 1 inch thick.
Place the patties on a parchment-lined plate. Refrigerate for 1 hour or place in the freezer for about 20 minutes to firm them up.
Preheat a grill to medium-high heat and generously oil the grates to help prevent sticking.
Place the patties on the hot grill. Cook for about 4–5 minutes per side, or until the burgers are no longer pink in the center, the juices run clear, and the internal temperature reaches 165°F (74°C).
Toast the hamburger buns while the burgers finish cooking.
Assemble the Best Turkey Burgers on the toasted buns with mayonnaise, cucumber slices, and thinly sliced red onion.
Serve immediately with your favorite burger sides.