I'm going to take this prompt two ways. (Didn't think I'd finish this, did ya?) Well, I am. One can understand "just" to indicate a small interval of time between conclusion and this writing. But! One can also think of it as indicating that finishing at all was a near run thing and only barely accomplished.
So, to take the latter first, I only just finished Anna Karenina. Don't misunderstand, the book is a triumph. The plot, characters, dialogue (even in translation) were all amazing. But the tale is so relentlessly depressing it's a long, hard slog to get through it. I think I probably read a half-dozen Wodehouse books interspersed with it just so I wouldn't get so down that I'd throw myself under a train. (Too soon?)
In the other sense, I think the most recently completed book I've read is Pandora by Holly Hollander by Gene Wolfe. Yep, you read that right. This is Mr Wolfe's foray into writing a detective novel. Not that none of his other stories have mystery, but I think this is the only novel which is entirely in that genre. The references are not quite as obscure, and it is typically brilliant, as Gene Wolfe's books tend to be.