There are a few rare bloggers I know of that write up their games like this.
Hack & Slash writes transcripts of his old-school games for illumination of the old-school playstyle and for self-improvement as a DM, as far as I can tell. You can read them all at Hack & Slash's transcript tag. There are only six as of this moment, but each one is extensive and reads like an authentic session transcript, "uhs" and everything.
An excerpt from a Hack & Slash transcript:
DM: Well, uh. The only thing you see under the planks is stale fetid water, and inside the pond, you see a giant floating frog corpse about five feet in length.
Rachel: Is in intact?
DM: Fairly intact, yes. It's in the water? So you would have to, I don't know, either get in the water or pull it towards you in some way.
Rachel: How far into the water?
DM: Well, the whole pond thing is maybe 25, 30 feet across, So 10-12 feet?
Rachel: I bet we could throw, what do you call them? One of our grappling hooks.
Garth: Do we want. . . a frog corpse?
Rachel: Well we might be able to figure out how the frog died.
[transcript continues like that]
Another I know is the Delvers. The style there is editorial, not the line-by-line transcript that you're looking for, only interspersed with quoted exchanges. However, I've yet to read a reconstruction of a game that felt more like what roleplaying is like. The editorial effort goes into helping the reader appreciate what it's like being player and DM in these games and on some choice player interactions, and the quality of the writing is such that it becomes transparent to the feel of the session. As a bonus, the entire blog is editorialised-transcripts and updated frequently, so you've got a mountain of material to choose from there.
An excerpt from the Delvers:
Looking back at the animal trophy, Alina and Circe realized this was no giant owl head. It was the head of an owlbear, slain by the two dwarves. It was the source of farmstead harassments of Eastbrook.
The rage in the owlbear’s dead eyes appeared to stare back at the celebrating farmers below it.
The girls had never heard of an owlbear. It was fun describing this creature to them for the first time.
Starlight: That thing is pretty cool.
Galem: Alive, it’ll crush you to death, if you’re not careful.
Starlight: Unless you’re too short to crush.
Galem: Look who’s talking.