Preheat a grill, grill pan or large non-stick skillet to medium-high. If using a grill pan or skillet, preheat the broiler.
Place the ground turkey in a medium bowl and season with salt and pepper. Add the lemon zest, parmigiano-regiano, finely chopped garrlic, spinach, thyme, and a drizzle of olive oil (about 2 tablespoons), and combine. Form into 4 patties and cook the burgers until firm and cooked through, about 6 minutes on each side.
If cooking the patties on a grill, place the bread alongside the patties, grill on both sides and remove. If using a grill pan or skillet, broil the bread on both sides until toasted. Rub the toasted bread with the remaining garlic. Place the bread on plates and top with a slice of tomato, then season the tomatoes with salt and pepper.
In the last two minutes of the burgers' cooking time, divide the sliced artichokes evenly among the burgers, then cover each with 2 slices of provolone. If cooking on the grill, drop the lid to melt the cheese. If cooking on the stovetop, tent your grill pan or skillet with aluminum foil. Place a burger on top of each of the tomato slices and serve immediately.