Rinse and drain spinach well. Cut off any large stems. In a small skillet, add olive oil over medium heat. Once hot, add spinach and cook until spinach is wilted, about 2 minutes. Set aside.
Divide ground beef into 4 oz. patties that are slightly thinner than a hamburger and roughly the shape of your bread. Season each side with salt and pepper.
In a sturdy skillet over medium heat, add a drizzle of oil and cook your patties for 4-5 minutes per side until they are cooked through. Remove from the skillet.
Add two pieces of lightly buttered bread to the skillet, buttered side down. Turn heat down to low.
Add mustard to the bread and top with the patty. Then top with a few slices of cheese and spinach. Top with second piece of bread, buttered side up.
Cook patty melt for 3-4 minutes per side until cheese is well-melted and bread is nicely toasted.
Remove patty melts, slice in half, and serve while warm.