Preheat the oven to 350*. Lightly grease a 2 quart casserole dish.
Using a large skillet,fry the bacon over medium high heat until crispy and brown. Place on a paper towel to drain. Add the butter to the same skillet and melt over low heat. add the squash and onion and cook for about 10 minutes, stirring continually until soft and slightly browned. Remove from the heat and cool.
Combine the mayonnaise, Parmesan cheese, eggs and 1/2 cup bread crumbs in a large bowl and whisk to combine. Add the squash mixture and basil, season with salt and pepper to taste and stir to mix.
Spoon the casserole mixture into the prepared dish, sprinkle with the remaining 1/4 cup bread crumbs, and crumble the reserved bacon on top. Bake for about 40 minutes, until bubbling around the edges, puffy and slightly soft in the center.