Slices that are 1/4-inch thick will cook evenly. If the slices are thinner (1/8-inch thick) they tend to burn easily. If the slices are thicker (1/2-inch thick), they take too long to become soft.
You can use either vegetable oil or olive oil. If you like the flavor of coconut, then go ahead and use coconut oil. Butter gives the dish a rich, buttery flavor that is delicious. However, you can choose to skip the butter for a lighter version that is still really flavorful.
For a savory version of this recipe, skip the cinnamon and instead sprinkle grated or shaved parmesan over the cooked squash. You can also add fresh herbs (rosemary, cilantro, parsley or chives) and/or spices (cumin, cayenne, curry powder).
Additional toppings for sautéed Delicata squash include pomegranate seeds and nuts, like pistachios, walnuts, pecans or almonds.