Melt the butter in a large nonstick skillet over medium heat. Add the hardy greens, scallions and jalapeños. Season with salt and pepper and cook until the greens have wilted, about 2 minutes.
Meanwhile, add the half-and-half, pesto and eggs to a pitcher or bowl. Whisk with a fork until well combined.
Add the egg mixture to the skillet and season with a pinch of salt and pepper. Cook, stirring frequently, until creamy curds begin to form, about 2 minutes. Add the Monterey Jack and continue to cook, stirring, until the eggs are just cooked and the cheese has melted, another 2 to 3 minutes.
Serve the eggs on top of the tomato slices and garnished with the chives.
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