Fry the bacon in batches in a frying pan until crispy, drain on kitchen paper, leave to cool, chop finely.
In a bowl, mix the flour, cheese, marjoram and salt with the bacon. Add the butter and rub together using your hands to form an even, crumbly mixture. Add the water, mix quickly to create a soft dough. Roll out the dough in two batches between two sheets of baking paper to a thickness of approx. 4 mm, cover and chill for approx. 30 mins. Cut out circles (each approx. 4 cm in diameter), place on two baking trays lined with baking paper.
Approx. 12 mins. per tray in the centre of an oven preheated to 200°C. Remove from the oven, allow to cool slightly, then leave to cool completely on a rack.
Combine the crème fraîche, marjoram and oil, season with salt. Serve the dip with the shortbreads.