For Sauce: In a small skillet set over medium-high heat, heat oil and paprika until oil shimmers and paprika is fragrant, about 2 to 3 minutes. Remove skillet from heat and let cool.
In the bowl of a food processor, combine parsley, oregano, red onion, garlic, and chili pepper flakes. Pulse to chop. Add vinegar and salt; pulse, and slowly drizzle in cooled oil with machine running. Chop until sauce is emulsified and chunky.
For Steak: Heat the olive oil in a well-seasoned cast iron skillet over medium-high heat. Season steak season well with salt and pepper. Place steak in skillet on the fatty edge and cook until the fat has rendered into the pan and the edge is brown, about 3 minutes. Turn and cook the other edge for 2 minutes. Now cook the wide sides of the steak until nicely browned, about 6 minutes per side for medium-rare. Remove from skillet and let rest 10 minutes.
Slice steak thinly, and serve with Chimichurri sauce.
Although the chimichurri can be refrigerated for a day, the sauce is best made just before eating, as the acid in the marinate will turn the parsley army-green if it sits for more than a few hours.
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