Put a rimmed baking sheet in the oven and preheat to 450 degrees F.
Combine the cream cheese, sour cream, garlic, lemon zest, salt, spinach and artichoke hearts in a food processor. Pulse until evenly combined. Add the mozzarella and Parmesan; pulse to combine.
Spread 1/4 cup of the mayonnaise over half of the bread slices. Place the slices, mayo-side down, on a second rimmed baking sheet and spread evenly with the spinach filling, all the way to the edges. Top with the other 6 slices of bread. Spread the top slices with the remaining 1/4 cup mayonnaise. Carefully, remove the hot baking sheet from the oven and place it directly on top of the sandwiches. Transfer the double-stacked baking sheets to the oven and bake until the sandwiches are golden brown and the filling is melted, about 15 minutes.
Let sit for 5 minutes before slicing into bite-size squares or triangles. Serve warm.