Step #1 In a bowl, whisk eggs, cream, & salt just until mixed; do not overbeat.
Step #2 Heat an 8-inch nonstick frying pan with sloping sides over medium-high heat for 1 min.
Step #3 When hot, add butter & tilt pan to coat evenly.
Step #4 When butter is foamy, pour egg mixture into pan & swirl to spread it out to edges of pan.
Step #5 As the egg mixture begins to set on the bottom, lift one edge with a heatproof flexible spatula & tilt the pan to let the uncooked mixture on top flow underneath.
Step #6 Continue lifting edges of omelet & tilting pan, working your way around all sides, until no more uncooked egg mixture will flow underneath & the top is just a little moist, about 2 mins total.
Step #7 Sprinkle top cheese either in a strip down the middle, if you plan on folding the omelet into thirds, or over one half, if you're folding it in half.
Step #8 Loosen the omelet with the spatula.
Step #9 For a third-fold, fold one edge over strip of cheese in the middle; tip pan to slide omelet, folded edge first, onto a warm plate, flipping remaining edge over filling as omelet leaves pan.
Step #10 For a half-fold, cheese side first, tip pan to slide omelet, onto warm plate; flip bare half over cheese as omelet leaves pan.
Step #11 Folding a plain cheese omelet:As egg mixture sets on pan bottom, lift edge with a spatula & tilt pan to let uncooked egg flow underneath.
Step #12 Continue the process, working around pan sides, until no uncooked egg mixture flows underneath & top is still moist.
Step #13 Sprinkle top cheese in a strip down the center of the omelet, in line with the pan handle.
Step #14 With the spatula, fold one side over the strip of cheese.
Step #15 Run spatula under omelet to loosen, folded edge first, & tip pan to slide omelet, onto a warm plate.
Step #16 Flip remaining edge over filling as omelet leaves pan.