Melt 3 Tablespoons butter in a skillet over medium heat and add the garlic and cook for a couple of minutes until the garlic becomes fragrant.
Turn heat to medium-high and add the spinach and stir for a couple of minutes until the spinach wilts.
Remove the spinach from the skillet with a slotted spoon (slightly squeezing the spinach as you are removing it) leaving any juice in the pan and set the spinach aside in a bowl.
Add the artichokes to the pan and cook over medium-high heat for several minutes. Cook until the liquid is gone and the artichokes begin to brighten up in color. Remove the artichokes, add to the bowl with the spinach and set aside.
In the same skillet melt the remaining 3 Tablespoons of butter.
Whisk in the flour and stir until it turns into a paste.
While stirring continue to cook for a minute or two. Add the milk. Continue to whisk until slightly thickened.
Add the cream cheese, feta cheese, parmesan cheese, ¾ cup pepper jack cheese, and cayenne. Stir until cheeses are melted and sauce is smooth.
Chop the artichokes and spinach and add to the sauce and stir.
Pour into a buttered baking dish or dishes.
Top with ¼ cup grated pepper jack cheese.
Bake at 375°F for 15 - 20 minutes or until cheese is melted and bubbly and the top is golden brown.
Serve with your favorite cracker, tortilla chip, fresh bread, or pita bread.