Crack the eggs into a small bowl and whisk vigorously until the yolks and whites are fully combined, creating a slightly frothy mixture. Season with a pinch of salt and pepper.
Heat the olive oil in a non-stick skillet over medium heat until it shimmers and just starts to smoke lightly, signaling it's ready.
Pour the beaten eggs into the skillet, tilting the pan to spread them evenly across the surface. Listen for a gentle sizzle and watch as the edges begin to set, becoming slightly firm and opaque.
Sprinkle the shredded cheese evenly over one half of the eggs, then add the chopped ham, bell pepper, and fresh herbs. Spread the fillings gently with a spatula to distribute evenly.
Allow the eggs to cook for about 30–40 seconds until the bottom is golden and slightly crispy, and the top is just beginning to set but still moist.
Carefully fold the omelette in half with your spatula, pressing gently to seal the fillings inside. Let it cook for another 10 seconds until the cheese melts and the omelette is heated through.
Gently slide the omelette onto a plate, letting it rest for about a minute so the cheese thickens slightly and flavors meld. Serve warm, garnished with extra herbs or hot sauce if desired.