Dry roast the walnuts in a small flat pan over a medium heat until they have toasted and turned golden brown. (Approx 3 - 4 minutes).
In a food processor add the walnuts, parsley, basil leaves, garlic, fennel, cayenne, sea salt and lemon juice. Process the ingredients adding the olive oil slowly while the motor is running until the pesto is well combined but not completely smooth. The pesto should still have a granular texture. Store in the refrigerator in an airtight jar ready for use.
Note: Due to their high fat content, walnuts can easily become rancid. Buy unshelled walnuts and select those that feel heavy for their size avoiding any with damaged shells. If you are buying unshelled nuts, check the date of packaging to ensure they're not old and only bulk buy nuts stored with a cover over them from a busy store with high turnover.