01 - Place Thai basil, cilantro, cashews, garlic, chili, lime juice, Parmesan, and sugar in a food processor or blender.
02 - Pulse several times until ingredients are coarsely chopped and well combined.
03 - With machine running, slowly drizzle in olive oil and sesame oil, blending until smooth but slightly textured paste forms.
04 - Add salt and black pepper, blending briefly to incorporate.
05 - Taste and adjust lime juice, salt, or sugar as needed for balanced flavor.
06 - Transfer to airtight container. Use immediately or refrigerate up to 5 days.