Palindromic palindrome generator
Dyalog APL, 6 4

⌽,,⌽


Try it here.

Other solutions:

⌽,⊢⊢,⌽
⌽⊢⊢,⊢⊢⌽


Explanation

They are just:

{⌽((,⍵),(⌽⍵))}
{⌽((,⍵)⊢((⊢⍵),(⌽⍵)))}
{(⌽⍵)⊢((⊢⍵),((⊢⍵)⊢(⌽⍵)))}


Monadic , and ⊢ does nothing on strings. Dyadic , is concatenation. Dyadic ⊢ returns its right operand. And ⌽ is obviously reversion.