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Heat olive oil in a medium skillet over medium/high heat. Add the chorizo and cook until brown and crispy. Once cooked, remove chorizo using a slotted spoon, and add to a small plate off to the side. Drain out most of the oil/fat and save a little bit for frying eggs in.
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Preheat the broiler of your oven to low. Line a large baking sheet with foil and set off to the side.
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Add the refried beans to a microwave safe dish and heat for about 40 seconds just to make them easier to spread.
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To construct the Mexican pizzas, start by spreading about 2 tablespoons of beans on a tostada, then a few tablespoons of cooked chorizo, and then finish off with another tostada. Top that tostada with a few tablespoons of red enchilada sauce and a good heap of cheese. Place finished pizzas on the prepared baking sheet.
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Once all the tostadas are prepared, pop them under the low broiler for a few minutes to melt the cheese.
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While the tostadas cook, fry the eggs up in the remaining chorizo grease.
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Remove tostadas from oven. Let them cool and set up for 3-4 minutes before slicing and serving. Best the day of.