Preheat oven to 350°. In a 10-in. ovenproof skillet, heat 1 tablespoon oil over medium heat. Add onion; cook and stir 3-4 minutes or until tender. Add garlic; cook 1 minute longer. Remove onion mixture from pan.
Add remaining oil to same pan; arrange potatoes on bottom of pan. Cook over medium-low heat 15-20 minutes or until tender, stirring occasionally.
In a large bowl, whisk eggs and milk. Stir in tomatoes, artichokes, onion mixture, 2 tablespoons goat cheese, 1 tablespoon fresh basil, salt and pepper. Pour egg mixture over potatoes; sprinkle with remaining cheese. Bake 25-30 minutes or until eggs are completely set.
Let stand 5 minutes. Sprinkle with remaining basil. Cut into wedges.