I always use cauliflower stalks for soup.
Wash them first, slice them and boil with other vegetables.
Strain soup, or blend it. If some of the stalks look thick and tough when you get as far as blending them, you can put them in the compost bin at that stage.
When making cauliflower curry, I use the thinner stalks, sliced finely and sometimes, if I feel they look a little tough, boil them seperately first then add them to the curry.
If you don't keep hens, rabbits, goats or pigs, it is shear waste just throwing the stalks out.