In a large non-stick skillet, over medium-high heat, add the chorizo. Cook, stirring and breaking up occasionally, until the chorizo is crumbly and completely cooked, about 5-8 minutes.
Remove the cooked chorizo to a paper towel-lined plate (to absorb the excess oil). Leaving about 1 tbsp of the chorizo oil in the pan, add the oven-roasted home fries and cook until crispy and heated through, about 3-5 minutes. Remove the potatoes to the same plate as the chorizo.
In a small bowl, beat the 4 large eggs and a pinch of pepper with a fork until very fluffy. Add the eggs to the same skillet. (Of there is no more oil in the pan, add 1/2 tbsp of oil or unsalted butter) Scramble the eggs until light, fluffy, and cooked all of the way through.
Add the potatoes and chorizo back to the skillet and stir until well mixed. Add the shredded cheddar and stir until the cheese has melted. Remove the skillet from the heat.
To plate: Scoop some of the chorizo-egg mixture onto the tostada shells. Top with any or all of the optional toppings. Enjoy!