Each clue gives a word or phrase that begins and ends with the same substring and has a single letter sandwiched in between. A few of the clues, such as 1950s British children's show, are more ambiguous and the solver must apply the sandwich constraint to help identify the correct answer.
|Piece of cake!"||EASY[P]EASY|
|Order in a library||SH[U]SH|
|2005 Great Big Sea subject||RIVER[D]RIVER|
|1950s British children's show||ANDY[P]ANDY|
|Wise Egyptian god||TH[O]TH|
|First name of a fashion designer||GIO[R]GIO|
Reading the single letters in the given order of the clues provides the solution, PULLED PORK.