Combine all ingredients except mayonnaise in a blender. Blend on high until smooth. If using a food processor, process all ingredients except the oil & mayonnaise for several minutes until smooth. Then add the oil and mayonnaise and continue to process until homogeneous. (I think a good blender or stick blender works best, but the sauce did come together using the food processor.)
3 jalapeños, 1 tbsp Aji Amarillo paste , 1¼ cups fresh cilantro, ¼ cup fresh basil leaves, 3 tbsp Parmesan cheese, 1 tbsp ginger paste, 1 tbsp honey, 2 cloves garlic, juice from 1 lime, 1 tbsp canola oil