How to make black peppercorns extremely fine?

Better grinding and sieving

If you think about it - spice powders are essentially flour. Pop it in a good blender. Blend, let it settle and sieve to required consistency. Repeat with oversized particles.

In an industrial setting this would likely mean a large mill and vibrating sieves, but you can, very carefully get the same results on a smaller scale. I believe some folks also use coffee mills for this, though obviously not one you have or intend to use for coffee.

For small quantities, you could probably use a spice mill or mill attachment on a blender. Just take your time.

Its also worth remembering a pepper mill cracks not grinds pepper.

An industrial grinding mill at a, uh, ground pepper factory (Caution! Extreme sneezing danger!) is not fundamentally different in design from your plastic store-bought mill. It consists of two hard surfaces which are very close together, and the pepper will be crushed and ground between them.

As Journeyman Geek mentioned, sieving will often be part of this process, but a good mill will be able to produce a very fine grind even without sieving. (In fact, sieving is usually used to remove dust so that the grind isn't too fine, not to exclude larger pieces.)

The store-bought mill you have, unfortunately, is not a good mill. The surfaces won't be kept a consistent distance from each other, meaning that large pieces of pepper will sometimes escape the mill. As the grinder wears down -- which it will, quickly, since the pieces are just extruded plastic -- it'll get even worse at this.

It is possible to buy really, really good spice mills, and you will pay a really, really high price for them. Much more practical is a coffee grinder. You can use either an upright blade-style grinder or a burr grinder... coffee purists insist on the latter, but that's because it'll produce less coffee dust, which is not something you're concerned about, and a blade-style grinder makes it easier to see and control the final grind. (Do NOT use one grinder for both spices and coffee. Grinders are not easy to clean. Your curry will taste of coffee and your coffee will taste of cumin.) Oh, and don't buy an antique-looking mill with the central spindle unsupported at the top -- these are very pretty but awful at grinding.

Mortar and pestles: Meh. There's a wide variety of those. The ones with a rough surface are fairly easy to use, but won't produce a fine grind. The smoother ones can grind hard, dry stuff to an infinitesimal grain size but will take forever to do so with plant matter like peppercorns. (If you must use one of these, add a bit of salt as an abrasive.)