Set a rack in the upper third portion of your oven and turn the broiler to high.
Place the artichoke hearts in a clean kitchen towel or several layers of paper towels and squeeze with your hands to remove as much liquid as possible, then roughly chop. Repeat with the spinach.
Heat a 10-inch cast iron skillet over high heat for 2 minutes. Add the olive oil followed by the chopped artichokes, and 1/2 teaspoon of the salt. Stir to combine, then press down with a large spoon or spatula and don't touch for 3 minutes. Then stir, press again, and cook until deeply browned, another 3 minutes.
Meanwhile, in a medium bowl, thoroughly combine the cream cheese, sour cream, mayonnaise, lemon juice, and half the garlic. Fold in half the parmesan and half the feta, and set aside.
Add the second half of the garlic to the artichoke mixture along with the red pepper flakes and cook for 1 minute, stirring constantly.
Add the spinach to the pan along with the remaining salt and cook for 1 minute, breaking up any clumps. Then, stir in the wine and cook until the pan is almost dry.
Kill the heat and stir in the cream cheese mixture. Smooth the top with a spatula then top with the remaining parmesan and feta.
Place the dip in the oven and broil for 3 minutes until the top is browned and bubbling, then serve warm with pita chips or crackers of your choice.