Preheat the oven to 400 degrees F.

In a saucepan over medium heat, melt 1/4 cup of the unsalted butter. When it turns bubbly, add the flour and cook, stirring constantly, until a blond roux is formed, 5 to 6 minutes. Whisk in the milk and bring the liquid up to a boil. Season with salt and cayenne to taste and simmer for 5 to 6 minutes, or until the sauce is thick enough to coat the back of a spoon. Remove the sauce from the heat and stir in the cheeses. Set the sauce aside.

In a sauté pan, heat the remaining butter. When the butter is hot, add the onions and sauté for 2 minutes. Add the spinach, a handful at a time, until all the spinach is incorporated. Add the garlic and artichokes and sauté for 4 minutes. Season the vegetables with salt and cayenne. Remove the spinach and artichokes from the heat and turn into a mixing bowl. Fold the béchamel sauce into the vegetables. Transfer the mixture to a baking pan and bake the dip for 10 to 15 minutes, or until the top is golden brown.

Serve the dip with chips or toast points.