I'm very new to this site, but a long-time pipe guy and would like to interject a comment or two. Right off the top, know that I'm a certifiable BURLEY FREAK...and like most guys I sure don't know everything, but I'm very opinionated! lol
So first: There are so many KINDS of burley blends available out there it helps to also try to define some additional perameters in what you're looking for. These are all my own terms, so try to put up with me...
There are soft blends...likley white burley plus something else...kind of natural aromatics...to me the classic examples would be Bluegrass and Nut Brown Burley (the latter is really lovely stuff...from McCranie's).
There are darker blends, maybe with a little added flavor (which most Burley's do have no matter what the label says - cause on their own most or a little flavorless) that form a "family" of what I think of as "Edgeworth-like blends...like Peretti's #300, Gray Havens, MacBaren's London Burley, that kind of thing.
There are burley flakes that are primarily burley like the Solani, Wessex and Peretti's BCP all are well regarded and rightly so.
There are burley flakes in which burley plays a role to a greater or lesser degree (and of course there are non-flake blends in the same vein). The choices here are myriad. Notable among them would have to be Exhausted Rooster...a flake of brilliant conception combining burley and perique. This is where I'd have to place the other C&D blends like Old Joe Kraintz, Haunted Bookshop, etc., etc., etc. There are also the Peterson trio of Irish, University and Perfect Plug - all are very fine and have their place. There are burley blends by Steve Brooks of Rich's in Portland, OR - this guy is incredible. What an astist!
Since I've already taken up far more space than I'm really worth I'll ask you to indulge me for just two further thoughts:
Depending on your experience with cigars and how strong in flavor and or potency you tolerate your pipr blends I have to mention some of the English plugs, ropes and twists. That's where I'm focusing my own indulgences at the moment - and am finding some amazing blends for the first time. Some years ago I tried Gawaith's Black Irish XX and was quite put off...then stayed away from the whole genre for a long time. Big mistake! There are amazing smokes amid the long list of possibles...not having to be flowerly, soapy or tasting like a campfire (though to be fair, most of those flavors will dissipate over time, I just want something I can smoke NOW as opposed to a year down the road).
I recently scored a kilo of Gawith's Dark Plug. It starts out smelling resinous and fire-smokey, but that goes away in just a few days of airing out and becomes a very fine, but very strong, smoke. So try it in a small bowl - I like it in my churchwarden and Falcon...but it works pretty well in any medium to smallish bowl. In addition to the plug, i have to comment on the Twists. The brown is great - I buy it pre-sliced. The Bogey is also very good. But my current discovery is the "flavored sweets" which aren't really very sweet, the addition of the flavoring just kind of take the edge off the pure brown taste (I think they're mostly based on the brown twist). I've tried the Sweet Rum Twist...stellar. I'm going to order the Whiskey, Maple and maybe even the Coconut! Don't laugh. The flavor is notable in the pouch and for the first few puffs...then it's GONE. And you're left with the brown base that is just fantastic...each, I'm assuming, special in it's own right.
So - I've saved the best for last. Try to find it. It's my favorite tobacco of all...dark, sweet, full, it's everthing! In a word...STONEHAVEN!
