What would it take for nature to produce asteroids composed of things like plutonium, uranium et al?

You've heard of the rarer type of asteroid then.
Most are made of much lighter stuff than the rare iron/nickel type.
Asteroids are composed of the dust clouds they condense from.
To get a high concentration of those rare heavy elements, the asteroids would
have had to form in the dust cloud from a supernova, (which produces the heavy elements),
and close enough to a hot new star, to drive off all the more common lighter ones.
Such asteroids would be very rare indeed anywhere and wouldn't be found in our solar system.

The heavier elements are produced by a super nova and then decay over time.   Asteroids have as much uranium as Earth does.   Neither Earth nor asteroids have plutonium, that's why solid core nuclear reactors were made, to produce plutonium.   That's why our current nuclear reactors such as Fukishima are so dangerous because they were designed to produce plutonium.   There were safer reactor designs such as molten salt reactors and gaseous core reactors but research for those where always cut despite their successes.

Yes, M-class asteroids are believed to be made of metal, mostly iron/nickel. It would take a protoplanet in the early solar system that got so large that heavier metals were differentiated out somehow, and you got solid metal meteorites of something other than iron/nickel when the protoplanet was blasted apart in an impact.

Is this even possible? It didn't happen in  our solar system, that we know. No meteorite has been found on Earth made of any metal other than iron/nickel. I think it's safe to say that the origin of the solar system is still so poorly understood that a definitive answer to your question isn't possible. It has been seriously proposed that the Earth has a inner core that is a five mile wide sphere of Uranium, so your idea isn't ridiculous:

http://www.spacedaily.com/news/earth-03k.html

Oh, and asteroids do contain large amounts of cobalt, gold, platinum, and rare earth metals, so the material was there, it just didn't get concentrated.

The universe started with hydrogen, some helium, and a trace amount of lithium.  Stars fuse hydrogen into helium, and in the later phases of their lives they fuse all the way up to iron.  An old massive star right before collapse would have layers (from outer to inner) dominated by hydrogen, helium, carbon, oxygen, silicon, and iron.  There is kind of a sweet spot between iron and lead, so in the very final phases of their lives stars can even make elements up to lead.  Only supernova explosions produces heavier elements in the moments after a supermassive star collapses.  Iron is the most stable atom so all smaller atoms become more stable through fusion, and larger atoms become more stable by fission.  

Thu upshot is that nature favours iron, and anything heavier than lead only exists in trace amounts.  All this stuff goes out into space as diffuse gas and dust, and must be collected back into a gas cloud before condensing into solid matter.  It is a mix of stuff, so there isn't likely to be large independent chunks of uranium and plutonium floating around.  It would more likely be in a solution of stuff like iron, magnesium, nickel, silicon, and lighter gases which would get blown off from small bodies.