How to Make It
In a small pan of boiling water, cook the potato and chayote until just tender, about 4 minutes. Drain the vegetables and transfer to a plate.
Heat the olive oil in a small skillet. Add the onion and red pepper and cook over moderately high heat, stirring, until wilted, about 2 minutes. Add the potato, chayote and garlic, season with salt and pepper and cook for 1 minute. Stir in the parsley and cilantro, cover and keep warm.
In a 10-inch omelet pan, preferably nonstick, melt the butter until the foam subsides; tilt the pan to coat the bottom and sides. In a bowl, combine the eggs and cream, and season with salt and pepper. Add the eggs to the pan and cook over high heat without stirring just until the edges set. Lower the heat to moderate and lift the sides of the eggs, tilting the pan to let the uncooked eggs spread underneath. Cook until the bottom is browned and the top is still slightly runny, about 2 minutes.
Spread the vegetables on top of the eggs. Tilt the pan and fold over one-third of the omelet to partially cover the vegetables. Roll the omelet onto a cutting board, flipping it over itself. Cut the omelet in half and serve on warmed plates.