What is your medium exactly?
You can't simply throw in egg shells, vegetable parts etc into a soil and expect it to immediately adjust nutrient quantity. It takes a lot of time for these things break down into the elements the plant can actually use.
To "amend it into a compost pile", you put the eggshells onto the compost pile, and let it do its thing until next year. Some people continuously stir their compost with a pitchfork or other mechanical means, but nonetheless, the eggshells have to break down before any benefits to the plants can be had.
What's the real problem you're trying to solve here? Sounds like an X-Y problem.