Preheat oven to 375°F.
Combine ½ Tablespoon of butter thoroughly with egg yolks.
Sprinkle cream of tartar on surface of egg whites and beat until stiff.
Fold egg yolk mixture into egg white until color appears uniform.
Heat remaining butter in an 8-inch omelet pan or heavy gauged, oven-safe sauté pan over medium heat; swirl pan to coat bottom of pan.
When the butter begins to foam and turn brown, add the egg mixture and sprinkle with the cheese.
Transfer pan to oven; bake 5 to 8 minutes, until omelet is set and springs back when lightly pressed in center.
Run a spatula around the edges of the omelet to loosen and gently slide and fold omelet on to individual serving plate.
For 2 servings, double ingredients and use a 10½-inch pan.