Clue: Boasting about a corgi dog that's cut out barking (11)
Answer: BRAGGADOCIO
Explanation: Definition: Boasting
An anagram ('barking') of 'abo[ut] a [c]orgi dog' with 'cut' removed ('out').* Actually it is [out] 'cut, not [cut] 'out': see rhotician @1, to whom thanks.