Note the whitish-grey area near the blossom. That's a very early indicator of the pending rot.
When you find this in your garden, just cut off the offending fruit and toss them. The plant will be fine and will likely produce other fruits that are just fine.
We've been eating lots of squash lately. I've been grilling them. Just cut 1/2" slices on a diagonal, toss with olive oil, and put them on a medium-heat grill for about 4-5 minutes per side. Top with salt and pepper for a fast and healthy side dish.