Melt the butter in a 10-inch nonstick skillet over medium heat. In a small bowl, whisk the eggs with a pinch of salt, then pour into the skillet. Cook, stirring constantly with a silicone spatula, until the eggs are set, about 2 minutes. Remove from the heat.
In another small bowl, crumble the queso fresco and mix with cilantro. In another small bowl mash the avocado with the lime juice and a pinch of salt. Spread the cheese mixture on the bottom halves of the buns and the mashed avocado on the top halves.
Divide the eggs between the two buns, season with salt and pepper, and top each with the tomato and onion. Add a dash of hot sauce, if using, then close the sandwiches and serve.
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