Set up your Big Green Egg for indirect cooking using the convEGGtor and preheat to 350°F.
In a bowl, combine olive oil, red wine vinegar, chopped parsley, chopped cilantro, minced jalapeño, minced garlic, and red pepper flakes to make the chimichurri.
Reserve about 1/3 of the chimichurri sauce for finishing the wings after cooking.
Place the chicken wings in a large bowl or resealable bag and pour the remaining chimichurri over them. Toss well to coat evenly.
Cover and refrigerate the wings for at least 4 hours, or overnight for best flavor.
Place the marinated wings on the grill grate over indirect heat.
Cook the wings for 45 minutes to 1 hour, flipping occasionally so they cook evenly and develop color on all sides.
Use an instant-read thermometer to check doneness and cook until the wings reach an internal temperature of 190°F to 195°F.
Remove the wings from the Big Green Egg and transfer them to a large bowl.
Toss the hot wings with the reserved chimichurri sauce.
Garnish with fresh chopped cilantro and sliced jalapeños.
Serve immediately while hot.