Line a sheet pan with a nonstick rubber mat. Pour some apricot purée on the rubber mat; spread it thinly with an offset spatula.
Bake until the purée can be peeled off the rubber mat, about 20 minutes. Tear or cut out rectangles about twice the size of the sablee. It is nearly impossible to get perfect rectangles, but try to get them as even as possible. Let cool to room temperature.
Store the apricot paper pieces in an airtight container at room temperature with silica gel packs to absorb moisture. If kept in dry conditions, they can last for up to 3 days.