Using a food processor, blender, or mortar and pestle, combine the fresh basil leaves, garlic cloves, anchovy fillets, Fresno chili pepper, ground coriander, ground fennel seeds, white pepper, and optional chili flakes.
Pulse or grind the ingredients until coarsely chopped, scraping down the sides of the bowl or mortar as needed.
With the food processor running or while grinding in the mortar, slowly drizzle in the extra virgin olive oil and lemon juice until the mixture forms a smooth sauce. Add more olive oil if needed to reach your desired consistency.
Taste the sauce and season with salt to taste. Adjust the seasoning or add more lemon juice for brightness if desired.
Transfer the sauce to a serving bowl or jar and let the flavors meld for about an hour. The flavors will develop and meld together as the sauce sits.
Store the sauce in the refrigerator for about 1 to 2 weeks in an airtight container. The sauce is at its best within 1-2 days of making.