Preheat a large skillet to medium-high heat with a pat of butter. When the skillet is very hot, add the artichokes in one layer with a sprinkle of salt and pepper. Let the artichokes char for about 3 minutes, then flip them and cook for two minutes more until browned. Remove to a plate and reduce the heat on the skillet to medium-low.
Add another pat of butter to the skillet, then add the spinach, garlic, and a pinch of salt and pepper. Use tongs to toss the spinach for about 2 minutes until wilted. Remove from the skillet to rest.
In the same skillet, add another pat of butter and place 2-4 bread slices into the skillet (you may need to make the grilled cheeses in two batches). Top each slice of bread with a slice of cheese and a thin layer of spinach and artichokes, using the ingredients evenly between the sandwiches. Top the veggies with another piece of cheese and a piece of bread to finish building the sandwiches. Use a spatula to press the sandwiches together.
Cook the grilled cheeses for about 4 minutes on each side until the bread is toasted and the cheese is melted. If needed, add another bit of butter to the skillet when you flip the sandwiches.
Serve hot. Enjoy!