Heat grill to high. Brush scallops on both sides with the oil and season with salt and pepper. Grill the scallops until golden brown and slightly charred and just cooked through, 2 to 3 minutes per side.
Spread about a tablespoon of avocado puree over each chip. Top the puree with a scallop and top each scallop with a dollop of the jalapeno pesto. Garnish with cilantro leaves.
Combine all ingredients in a food processor and process until combined, but still chunky. Puree until smooth, if desired.
Combine cilantro, jalapeno, garlic, pine nuts, salt and pepper in a food processor and process until coarsely chopped. With the motor running, slowly add the oil and process until emulsified. Scrape into a bowl.