Combine the artichokes, sun-dried tomatoes, mayo and 1 teaspoon of garlic in a blender or food processor. Pulse to chop roughly and combine. If you like a smoother spread, continue to blend until smooth. Season to taste with salt and pepper. Cover and refrigerate until needed.
In a large bowl, combine the ground beef, the remaining tablespoon of garlic and the chopped shallots. Season with salt and pepper, then mix lightly. Shape mixture into 4 equal-sized patties.
Heat oil in a large skillet over medium-high heat. Place the patties in the skillet, and cook until browned on both sides and cooked to your desired doneness, about 5-6 minutes, flipping once. Top each patty with the cheese during last 2 minutes of cooking.
To assemble - Toast your buns if you like, then spread some of the spread on the bottom bun. Top with arugula, then a patty. Spread more of the spread on the top bun, then place on top of the burger. Enjoy!!