There's not much of a direct path for what you're suggesting unless you're already a prospective owner or regular client for that category of aircraft. If you ferret around and try hard enough you might be able to find someone willing to sell you some dual time, but usually turboprop owners don't need a few extra grand in their pocket, and there's a lot of liability concerns with a low-time private pilot at the controls. And along with that, of course, are insurance considerations.
Most pilots who want to fly kerosene burners are on a career path. If you're not, and you don't own a multi-million dollar business or have some kind of comparable income stream, these types of aircraft are mostly off-limits to you; even single-engine turboprops. By the way, I don't think you're missing much until you get into jets. Flying a turboprop single isn't really that much different from flying a high-performance single. Just higher altitudes and true airspeeds.
). 
