Combine 1/4 cup of vegetable oil and flour in a saucepan over medium heatl. Stir the mixture constantly for 5-6 minutes to make a blond roux. Whisk in the milk and bring the liquid up to a boil. Season the liquid with salt and cayenne pepper. Simmer the liquid for 5-6 minutes, or until the liquid is thick and coats the back of a spoon. Remove the sauce from the heat and stir in the cheeses. Set the sauce aside.
In a saute pan, heat the remaining vegetable oil. When the oil is hot, add the onions and saute for 2 minutes. Stir in handfuls of spinach at a time, until all spinach is incorporated. Add the garlic and artichokes and saute for 2 minutes. Season the vegetables with salt and cayenne pepper. Remove the vegetables from the heat and turn into a mixing bowl. Fold the reserved cheese sauce into the vegetables. Turn the mixture into a baking dish. Bake the dip for 10-15 minutes, or until the top is golden brown.