Stir together first 5 ingredients, 1/2 teaspoon salt, and 1/2 teaspoon pepper. Set aside.
Drain artichoke hearts, reserving oil. Coarsely chop artichokes. Stir together artichoke, reserved oil, chopped 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 sauté 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.
Layer one-third of noodles, half of ricotta cheese mixture, 1/2 cup cream sauce, and half of avocado mixture into a lightly greased 13- x 9-inch baking dish.
Repeat layers once, ending with remaining noodles and remaining cream sauce. Sprinkle with remaining 1/2 cup Parmesan cheese.
Bake, covered, at 400° for 40 minutes. Uncover and bake 5 more minutes or until lightly browned. Let stand 15 minutes.