How to Make It
Scoop the avocados into a small bowl. Using a fork or spoon, lightly mash the avocados with the chiles, 1 teaspoon of the olive oil and a generous pinch of salt. Spread the avocados on the two pieces of matzo.
In a medium skillet, heat the remaining 1 tablespoon of olive oil over moderate heat. Crack the eggs into the skillet and cook until the whites are just barely set. Add the butter and cook until the desired doneness. Transfer the eggs to the matzos and season with salt and pepper. Top with the basil and serve.