Heat grill to medium-high; lightly oil it. Grill jalapenos until slightly charred and blistered, turning frequently, about 15 minutes. Using a paper towel, pull off stems and remove skins from chiles. Roughly chop flesh and seeds; set aside. Place 2 cups blueberries in a food processor; pulse until coarsely chopped, about five times. Transfer to a medium bowl, and add onion, jalapenos, lime juice, and 1/4 teaspoon salt; stir to combine. Add basil, cilantro, remaining blueberries, and oil; stir to combine. Try with grilled chicken.