Combine the chicken wings, 1/4 cup of the olive oil and paprika in a large bowl, sprinkle liberally with salt and pepper then toss until evenly combined. Refrigerate for at least 2 hours or up to overnight.
Meanwhile, make the chimichurri: Combine the vinegar, garlic and a generous pinch of salt in a blender and blend on low until smooth. Add the parsley, cilantro, oregano, ice and jalapeno and blend on medium speed. With the blender running, slowly drizzle in the remaining 1/4 cup plus 2 tablespoons olive oil and puree until smooth, about 1 minute, stopping to scrape down the sides if necessary. Season the chimichurri with more salt and pepper and transfer to a serving bowl, cover with plastic and refrigerate until ready to serve.
Preheat a grill to medium. Brush the grill grates with vegetable oil. Grill the chicken wings, turning every 6 minutes, until golden brown, lightly charred at the edges and cooked through, about 25 minutes.
Transfer the wings to a serving platter and season with salt to taste. Drizzle with some chimichurri sauce and serve the remaining sauce on the side.
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