This is a fly from the genus of “Hanging thieves” (Diogmites) in the family of Robber flies (family Asilidae). On sweet basil (which seems to attract a lot of insect activity as well as be the main ingredient in Clare's homemade pesto).
Explanation of names, from BugGuide, http://bugguide.net/node/view/4600 »
Diogmites comes “from Greek διωγμοσ ‘chase, pursuit’. The common name was suggested by Herschel Raney after Dogmites's habit of hanging by its forelegs while consuming prey.”
Retired economics professor (“dismal scientist”). Married 40+ years to the love of my life; we have two grown daughters, both married, two granddaughters and a...