Melt butter in a skillet over medium heat. Add minced garlic and cook for two minutes. Whisk in flour until a paste forms. Cook over medium-low heat for 1 minute, then pour in milk. Stir and cook one minute. If your paste gets too thick, add a little more milk to thin it out slightly. Add cream cheese, mozzarella, Parmesan and pepper. Stir until cheeses are melted. Whisk in Greek yogurt until sauce is smooth. Fold in chopped artichokes and spinach.
Heat a skillet or griddle to medium-low heat. Butter the outsides of each slice of bread then spread 2-3 Tablespoons of the cooked dip on one slice of bread and top with another, with the buttered sides of bread on the outside. Cook sandwich until both sides of the bread are golden brown.