Preheat oven to 400°F. Combine garlic and wine in a small saucepan over medium heat. Simmer, stirring occasionally, until wine is reduced by half, about 10 minutes.
Combine wine mixture, cream cheese, mayonnaise, artichokes, spinach and 3/4 cup Parmesan in a food processor. Season with salt and pepper. Pulse until artichokes are coarsely chopped.
Spoon into a 1-quart shallow baking dish and sprinkle top with remaining 2 Tbsp. Parmesan. Bake in middle of oven until golden brown on top, about 30 minutes. Serve immediately with crackers or toasted bread.