How to brown ground beef so it comes out uniform and not chunky?
To help get uniformly broken up ground beef:


Choose an at least moderately fatty (say 80-85%) grind, as very lean ground beef will tend to stick to itself more.
Don't compress it when you are bringing it home, as by setting other groceries on top.
Don't salt the meat before cooking, as salt tends to help it bind to itself.
Break it up into chunks with your finger as you put it in the pan to brown.
Don't raise the heat too high, which leaves you less time to break it up as it browns.
While it cooks, frequently break up chunks with your spoon or spatula


The real key is the last one.

There is always going to be certain variability in the size of chunks, unless you are very vigilant in breaking up the pieces fairly continuously.  

If you cook it in water, as per Cincinnati chili, you can get it very broken up, but it will be a different texture.