In a small hot skillet, saute the mushrooms in olive oil. Add the chopped garlic and then deglaze the pan with red wine vinegar. Remove from the heat and cool. Meanwhile, in a large bowl, mix together the watercress, carrot, red bell pepper, and jicama. Add the cooled mushrooms and toss lightly to combine. Set aside.
To flatten the steaks, coat 4 (15 by 12-inch) sheets of plastic wrap or parchment paper with 1/2 teaspoon of vegetable oil each. Sandwich each tenderloin, with the grain running vertically, between 2 sheets (with the oiled side facing the meat). Flatten each steak with the flat side of a heavy cleaver or mallet, using steady, even sweeping strokes from the center out as you would roll pie dough, until the steak is a thin oval of about 14 by 10 inches. It should be thin like a blanket, hence the name sabana. This process takes about 5 minutes per steak.
Preheat a lightly oiled very large nonstick skillet or cast-iron pan over high heat. Peel the paper off the steaks and brush both sides with the Chimichurri Dressing. Sear steaks, 1 at a time, in the hot pan, about 1 to 2 minutes per side. The cooking time will not be long because the steaks have been pounded so thin.
Melt the butter in a small hot skillet. Crack the eggs into the pan and season with salt and pepper, to taste. Cook eggs sunny side up.
To serve, place 1 steak on a large serving plate. Toss the salad with the remaining Chimichurri dressing to coat; serve the salad over the steak. Slide a fried egg on top of each and serve.
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