To bring that burnt caramel taste in your beer, you'll be looking to add some seriously high crystal malts, 120 or even 150. British crystal apparently adds a more pronounced and better flavor than american crystal, although I haven't tested myself, so if you can get your hands on that it would be great!
By using a low attenuating yeast (english types in general are relatively low), you'll be able to achieve that somewhat sweet, caramel-y flavor you want. I learned a lot reading (and to some extent testing) about the different crystal malts and what they add to the beer in terms of flavor. Just be sure to balance the recipe according to style if you're not used to brew a good classic oatmeal stout to begin with and you should end up with a pretty good product!
Good luck!