How to create something that can randomly generate in existing generation?

To start with, I think grass regrows randomly after world generation, right? (grass and tall grass, not the dirt block becoming green). if this is true, my first idea was to piggie back off of grass and make a new grass type. I did this, and even with setting the frequency to 1, this new "grass" is literally everywhere!

so, the other option was to find out if there is just some way to do what I want, without grass. I want to create a new block that will, in a performant way, randomly, and infrequently, spawn anywhere in the world, on top of specific blocks (grass, sand)