When the butter is softened, (see video on how to test if butter is ready for baking), beat a little with a hand/stand mixer until soft & spreadable. Add in the icing/powdered sugar & salt, beat again but only just until incorporated. (See Photo 1 below). Then mix in the egg yolk & oil. Next add the bicarbonate of soda (baking soda) to vinegar in a small bowl, (but not too small as the mixture will react and fizz). Be sure to be ready to quickly add this to the main mixing bowl, before giving it a mix through till incorporated. See Photo 1 above.
Gradually add the flour, until a smooth dough comes together. I usualy add in about 125g (1 cup) of flour at a time. You might need more or less flour. Different types of flour, where & how it is milled, results in a variation in how much liquid it will absorb. So there can be no exact amount of flour to add with lots of recipes. For the correct consistency, roll a smooth ball of the dough & flatten it with your hand. If you do that without it falling apart or sticking to your hand, it is ready. You can also swap over to a wooden spoon/spatula or use your hands, towards the end of bringing the dough together. See Photo 2 above.
Cut 2 extra large pieces of baking/parchment paper (approximately 40cm/15½″ long). Knead the dough for 5 second knead & shape into a ball & flatten. Place the cubed cheese in a food processor & blitz to large breadcrumb sized pieces. Alternatively you can just add grated cheese (I have done this when I have forgot). Add the cheese to the top of the disc of dough & knead together, just until all the cheese is distributed. (You can do this on the paper or whilst still in the bowl). See Photo 3 above. Divide the dough, & flatten both into a disc, placing one half into the fridge in some paper or cling film/plastic wrap.
Place one half of the dough, in-between the 2 sheets of baking/parchment paper, before rolling the dough until you a thickness at least 5 or 6mm (⅕-¼"). (*height of £1 coin plus a 1p). Place the rolled out dough (& bottom paper), on a tray & place in the fridge, making sure it is completely flat. Chill the dough for 30 – 45 minutes**, while doing the same for the second half of dough. (Take a note of when you placed the first rolled out dough into the fridge). See Photo 3 above.