Stir together first 5 ingredients, 1/2 teaspoon salt, and 1/2 teaspoon black pepper. Set aside. Drain artichoke hearts, reserving oil, and coarsely chop. Stir together artichoke, reserved oil, avocado, green onions, and remaining 1/2 teaspoon salt and 1/2 teaspoon pepper. Set aside. Melt butter in a medium saucepan over medium-high heat; add garlic, and saute 1 minute. Add flour, whisking until blended; cook, whisking constantly, 1 minute. Gradually whisk in whipping cream. Cook, whisking constantly, 3 to 4 minutes or until thickened and bubbly. Stir in 1 cup Parmesan cheese.