Beat eggs, cheese, parsley, marjoram, thyme, salt, and cayenne pepper together in a small bowl with a fork until combined.

Heat olive oil in a small, nonstick skillet over medium heat. Pour egg mixture into the skillet; cook and stir constantly, scrambling eggs using a rubber spatula, scraping the sides of the skillet as needed.

Reduce heat to low when eggs start to come together; continue cooking, stirring slowly but constantly, until eggs are very wet and softly scrambled. Turn off the heat.

Tilt the skillet toward you; push eggs together at the bottom edge of the skillet. Tuck in and smooth out eggs' edges with your spatula as you form eggs into an omelet that is no longer wet, but still moist.