For the leek crema: Using only the lower third of the leek, remove the root, cut lengthwise down, then dice. Melt the butter in a small saucepan over medium heat. Add the leeks and 2 tablespoons of water. Cover and cook, steaming the leeks until very tender, about 5 minutes.
While the leeks are steaming, slice the squash lengthwise to ¼-inch thick slices on a mandoline or with a knife, and set aside. Finish the leek crema by adding salt, then cream, and warm through.
For the squash casserole: Preheat the oven to 400 degrees F. Coat a 9" x 9" or 8" x 10" casserole dish with the butter by rubbing it as if you were waxing a car. Arrange the squash in a single layer in the dish. It's all right if you shingle and overlap edges minimally. This is a six-layer casserole, so allocate the ingredients accordingly. Evenly coat the first level of squash with a ladle of crema, a pinch of salt, a pinch of pepper, a bit of thyme, a sixth of the breadcrumbs, and a sixth of the Parmigiano. Repeat these steps 5 more times, then cover the casserole with a fitted lid or foil. Bake covered for 35 minutes, then uncovered for 10 more minutes or until the top becomes nice and golden brown.
Remove casserole from the oven and allow to cool for 10 minutes before serving.