Heat 1 tsp of butter in a large non-stick skillet over medium heat. Add minced garlic and sauté until golden and fragrant, about 30 to 60 seconds. Then, add in spinach and artichokes, season with salt and sauté until the spinach wilts.
Transfer the mixture to paper towels and squeeze out excess moisture. This step is crucial to prevent sogginess.
Butter the outsides of the slices of bread. On the non-buttered side of three slices, layer half the provolone cheese, then the spinach-artichoke mixture, dollops of sour cream, and sprinkle remaining cheese on top. Top with the other slices of bread, buttered side up.
Heat the skillet over medium-low. Place as many sandwiches as you can fit in the skillet. Cover with a lid and cook until golden brown, about 3 to 5 minutes.
Carefully flip the sandwiches, cover, and cook until the other side is golden brown. Keep an eye on them to avoid burning.
Repeat with any remaining sandwiches. Serve immediately while hot and gooey.