In a small bowl, mix mayonnaise, sun dried tomatoes, and ketchup. Cover and place in fridge.
In a large skillet, melt butter over medium-high heat. Add garlic, onion, pepper, and mushrooms and saute until onions are clear and tender. Add spinach and continue to cook mixture until spinach is defrosted. Remove from heat.
In a large mixing bowl, combine cooked vegetables with feta cheese, salt, and beef.
Make 8 patties by dividing meat into 2/3 cup portions and then flatten to about 1/2 inch thick.
Preheat grill to medium-high and meanwhile fry ham slices in a non-stick pan over medium-high heat for 1 minute on each side. Place fried ham on a plate and cover with foil to keep warm.
Grill patties (about 6 minutes per side) and place a slice of provolone cheese on each patty for the last minute. (Feel free to butter the inside of the bun and throw it on the grill to toast for the last minute as well.)
Assemble burgers: On buns, layer with grilled patty, fried ham, a few spinach leaves, and sun-dried tomato mayo slathered on the inside top bun.