In a large mixing bowl, or stand mixer, mix together the warm water, yeast and sugar. Let it stand for 10 minutes until the mixture bubbles and grows.
Add the salt and oil. Knead in the flour, 1/2 cup at a time, until the dough pulls away from the sides and is not too sticky. Knead for 5-10 minutes, until the dough becomes smooth and elastic. Cover the bowl and let the dough rise for 1 hour, or until doubled in size.
While the dough is rising, make the shortbread by mixing together the butter, powdered sugar, salt, flour and vanilla until fully incorporated. The mixture will be crumbly. Dump the shortbread into a greased 8x8 pyrex dish. Spread and push dough the mixture to the edges and create a dough of even thickness in the dish. Bake at 350 degrees F for 15 minutes or until the edges are golden brown. Allow the shortbread to cool in the dish while making the lemon curd.
To make the lemon curd, add the sugar, lemon juice, eggs, flour and lemon zest into a pan and whisk together until fully incorporated. Heat on medium heat, whisking often, until the mixture thickens and can coat the back of a spoon. The mixture will burn easily so watch it closely!
Once thickened, remove the lemon curd from the pan into a small mixing bowl and place in the refrigerator until ready to use.
Once the dough has risen, remove it from the bowl onto a clean surface and roll the dough into a large rectangle about 1/4 inch thick. Spread the lemon filling evenly across the dough, leaving about 1 inch around the edges of the dough.
With a fork, crumble the shortbread into small to medium crumbs and sprinkle on top of the lemon filling. Roll the dough cinnamon roll style, lifting the dough slightly as you roll to prevent the lemon filling from being squeezed out. Slice the dough to create 1 inch thick rounds and place on a greased baking sheet about 1 inch apart. Cover the rolls and let them rise for about 45 minutes or until doubled in size. Bake at 350 degrees F for 15-25 minutes or until the rolls are golden brown. Allow them to cool in the pan for about 10-15 minutes.
While the rolls are cooling, make the lemon icing by beating together the butter, lemon juice, vanilla, salt, lemon zest and powdered sugar. Add the powdered sugar 1 cup at a time and beat until the icing is fluffy. Spread the icing evenly over the rolls. Tear off a roll and enjoy!