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It was like a scene out of the jock version of "The Notebook" ...

Vin Scully and Yasiel Puig spotted each other from across the street in Beverly Hills on Monday -- and made their way toward each other ... culminating a HUUUUUGE bear hug.

And it might be the sweetest thing ever.

Of course, Scully retired as the voice of the L.A. Dodgers before the 2017 season -- but he was always fond of Puig. You can really feel the love when you watch the clip.

There's a moment when a waiter interrupts and asks Vin to sign his hat. Vin asks if he's a friend of Puig. The waiter says, "No, I'm a friend of Joe Torre." Vin signs anyway.

After the reunion, we talked with Puig about some Dodger topics -- and he was super cool ... until he noticed our guy was wearing a St. Louis Cardinals hat.