Neighbor Squash

My neighbors have this monstrous squash vine which has totally taken over our grassy alleyway. When I step over it on my way to the co-op I get a Jumanji-style chill up my spine. Not really, it's gorgeous and prolific, with giant yellow blossoms and huge, strange pale green globes lurking in the growth. 

I talked to the mom, Mary, and she said a friend-of-a-friend had given her the seeds and she didn't know what kind. We both speculated on when the squash was ready for picking... when it's darker green, or was it already past prime since they were so gigantic? I gave her a recipe from the Joy of Cooking for stuffed squash blossoms, and she picked one squash and gave me half.

I baked it till it was soft, and cut it up (light yellow on the inside, with big, meaty white seeds) for thai green curry with cashews. It was creamy and with a delicate flavor. Still no idea what kind it was, though. I'd love to find out.