Mix butter, sugar, flour, walnuts, rum and salt till well combined and smooth. Refrigerate for 2 hours.
Preheat oven to 180 C / Gas 4. Line a baking tray with greaseproof paper.
Roll out mixture in batches on a floured surface and cut out biscuits of the same shape. Bake for 10 to 15 minutes. Let cool.
Push apricot jam through a fine sieve and brush half of the biscuits with it. Place a second biscuit on top. Dust with icing sugar if desired and store in airtight tins.