In small bowl combine eggs, half-and-half, salt and pepper. Beat together with fork 1-2 minutes until solid yellow and no longer streaked. Do not over-beat and cause bubbles.
Melt butter in pan and pour in half of egg mixture. Cook about 1 minute. Then gently lift up edges while tilting pan in that direction, do this all the way around the omelet. This allows uncooked egg on top to cook more evenly. Once bottom is mostly set and no longer breaks when lifting edge (the top will still be slightly runny), add half of the green onion, goat cheese, spinach and tomatoes to one side.
Take off of heat and cover with lid to evenly cook omelet and vegetables, about 1-2 minutes more. Once egg is set and spinach slightly wilted, fold half over to form complete omelet.
Remove omelet from pan (place plate on top of pan, then flip pan over plate to cleanly drop the omelet on the plate). Repeat process for second omelet.