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Step 1
To make the secret sauce, combine the tomato paste, water, orange juice, Spanish paprika, cumin, brown sugar, vinegar, salt and sriracha in a small sauce pan. Bring the mixture to a boil and then reduce the heat to a simmer. Simmer 15 minutes or until the sauce has thickened slightly.
Step 2
To make the fries, heat 2 to 3 inches of oil in a heavy-bottomed pot to 350 degrees F.
Step 3
Carefully cut the potatoes into shoestrings (or matchsticks) using a mandolin fitted with the narrowest julienne blade (about 1/8-inch wide) or just use your knife (this is what I did). Rinse the cut potatoes thoroughly in a bowl of cold water to remove the surface starch. Keep the potatoes in water until you're ready to fry. (I like to begin frying mine while the burgers are cooking)
Step 4
To form the burger patties, combine the beef, chorizo, ketchup, Spanish paprika, cumin and a pinch salt and pepper in a bowl and mix until just combined. Form the meat into six patties.
Step 5
Heat a large cast iron skillet or griddle over medium-high heat. Cook the burger until your desired doneness, but traditionally Fritas should be cooked to medium. During the last minute of cooking, add a slice of cheddar cheese.
Step 6
Meanwhile, fry the potatoes, transfer the potatoes to a paper-towel-lined baking sheet and pat them dry, as dry as you can get them.
Step 7
Fry the potatoes in batches until the potatoes are crisp and turn a nice golden brown, 2 to 3 minutes per batch. As each batch of fries comes out, transfer to a large mixing bowl and toss with salt to taste. Transfer to a paper-towel-lined baking sheet.
Step 8
Serve the burgers on warmed Cuban buns that have been slathered with a little special sauce. On to the bottom bun, place the burger, fries, more special sauce and top with a fried egg. Place the top bun over the egg, grab the burger with two hands and EAT!