Preheat broiler. Beat first 4 ingredients in large bowl to blend. Spray oven proof 10-inch nonstick omelette pan, heat over high heat. Pour 1/2 cup egg mixture into pan and cook until almost set, tilting pan and lifting egg mixture with rubber spatula to allow uncooked portion to run underneath, about 1 minute. Do not allow to brown.
Spoon 1/4 of crab over right half of omelette, sprinkle 1/4 of green onions, 1/4 artichokes, 1/4 basil and 1/4 of cheese over crab. Season with salt and pepper. Place pan under broiler until cheese begins to melt about 15 seconds.
Fold left side of omelette over filling. Slide omelette onto warm plate. Wipe pan with towel; repeat.