Make the chimichurri sauce. Combine the chopped parsley, cilantro, dried oregano, shallot, grated garlic, aleppo, and red wine vinegar together in a bowl. Whisk in the olive oil and season to taste with salt and pepper. Transfer half of the chimichurri sauce to a large mixing bowl.
Marinate the shrimp. Add the uncooked peeled and deveined shrimp to the mixing bowl with the chimichurri sauce and toss well to coat. Cover the bowl with plastic wrap and marinate for 1 hour.
Make the whipped feta. In the bowl of a food processor, add the feta, greek yogurt, garlic, lemon zest, lemon juice, and aleppo pepper. With the mixer running, stream in the olive oil until the feta is very smooth and easily spreadable. Season to taste with salt and pepper and set aside.
Preheat a grill. Before using your grill, make sure to clean the grates of any food and debris. Lightly grease the grates with nonstick spray. Preheat your grill to medium heat. If you’re using charcoal, move all the hot coals to one side. Close the lid and wait at least 15 minutes, until the temperature reaches 450 F.
Prep and grill the shrimp. Thread the marinated shrimp onto grilling skewers in groups of 3-4. If you're using thin wooden skewers, be sure to soak them in water beforehand. Once your grill is preheated, place the shrimp on the grill, making sure there is space between each skewer. Close the lid and grill 3-4 minutes per side, until nice grill marks form. Remove the skewers from the grill and transfer to a serving platter.
Serve the shrimp. Drizzle the grilled shrimp with the remaining chimichurri sauce and squeeze lemon wedges over the top. Serve the grilled shrimp with the feta sauce while warm.