I wrote a Data Explorer query that does this. You can search the body of answers given to your questions. As the data explorer gets updated weekly, this is a workable solution till advanced search gets an update (if).
SELECT 'site://a/' + CAST(P1.Id AS nvarchar) + '|' + P2.Title as 'Post Link',
P2.Score as 'Score',
P1.Body as 'Content'
FROM Posts as P1, Posts as P2
WHERE P2.Id = P1.ParentId and --Join of Questions with Answers--
P2.PostTypeId = 1 and -- P2 Contains Questions --
P2.OwnerUserId = ##UserId## and -- P2 contains posts of User --
P1.PostTypeId = 2 and -- P1 contains Answers --
-- Search Parameters --
P1.Body like '%'+ ##SearchTerm:string## +'%'
--Searching Answer Body--