An ancient custom of serving guests an offering of food with a portion removed.
The custom served dual purposes. Symbolically, it was meant to indicate that nothing would be offered which was not equal to the servers own.
Practically, it allowed for a taste test to gauge the quality of the ingredients and preparation.
Our host explained that the pie was missing a piece to show that the house tested the pie to confirm it was good enough for you, which is the Scottish promise.