Preheat the oven to 325°F.
Sauté the onion in 2 tablespoons of olive oil with about ½ tsp of salt on medium high heat. Sauté, stirring frequently, until softened. Expect about 5 minutes.
Add the garlic to the pan, and sauté for another minute or two.
Add the grated squash to the pan along with another ½ teaspoon of salt. Sauté until the squash is reduced and has a creamy texture. This should take about 15 minutes total. Early on you should be able to see the water pooling under the squash as it poaches in its own juice. Over time the sweating will slow down, the water will steam off, and the squash will reduce.
While the squash sautés, beat the eggs with the cream, ½ tsp of salt and a few cranks of the pepper grinder.
Evenly distribute the vegetables in the pan and pour the egg mixture over. Give a quick stir to suspend some of the vegetables off the bottom of the pan. Sprinkle the cheese evenly over the top (don’t skimp at the outer edge!).
Transfer the pan to the pre-heated oven and cook until done. Timing will vary for various reasons. Other than the true oven temperature, the biggest variable is the amount of seasonal vegetables that are in the pan. As they have just completed cooking, they hold a lot of heat. The more of them, the quicker the cook. Start checking for doneness after about 10 minutes. There should be no jiggle if you shake the pan. A toothpick test can reveal if there is any runny egg. You are going for a custardy egg. Too little time is runny and too much time is rubbery.