Shortbread dough is often crumbly because a traditional recipe uses no egg to bind the ingredients. Also, traditional shortbread would be pressed into a mould before baking, which would constrain the dough and keep the crumb dense. read more
Shortbread is a very simple recipe, just flour, butter and sugar. Look for a recipe that gives you amounts by weight, rather than volume. A scooped and leveled cup of flour can weigh anywhere from 4 oz to 5 oz, and the difference will matter in a recipe. read more
classic shortbread proportions are 3 flour, 2 butter, 1 sugar. I cream 3oz sugar with 6oz butter, then mix in 8oz plain flour and 1oz cornflour/ground rice. I find this way doesn't make it so crumbly, though my mum does the 'rub it in together until it clumps' method and her shortbread usually works too. read more