I grew up with Big Bob Gibson's just a short drive away. My Grandmother would sometimes pick up a Brunswick stew from them in a re-used gallon milk jug.
But, if you want state iconic barbeque, then Dreamland was the place. It started in Tuscaloosa, and when I used to teach at UA, everyone had to eat there at least once. At the original location in a shack on Watermelon Rd, the only thing on the menu was a slab of ribs, and any drink you wanted as long as it came in a can. White bread was always on the tables. That was it. You ate at the long slab picnic style tables with dogs roaming through the place begging bones off of people. I kid you not. Everyone would be covered in sauce and grease.
Now, they have a more upscale chain, but it's not nearly as delicious as the original. My oldest is working her way through college, at one of the chains. They are much nicer place than the original shack full of hungry dogs.
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Pictured is Big Daddy who owned the place, and he always had a pipe, and you walked into the shack, with no real door. And, he would be standing behind a makeshift counter, and the only thing he said was, "how many slabs?" And, you grabbed a drink out of one of many old kitchen refrigerators lined up, and paid, set down, and ate with your eyes rolling back into your head. The best ribs ever.
It's good now, but the fancy waitresses and other stuff on the menu, cleanliness, and the actual door, and no dogs... seems to have killed the mystique, ha ha. Back in the day when the restaurant inspectors didn't care a bit about what happened out of Watermelon Rd. It was a favorite place of Coach Bear Bryant as well, and all of the old football stars had eaten there many times over the years.
And, there's a pipe involved. If anyone goes to the chain store in Birmingham, please tip well.