Heat oven to 450?F. Prepare Batter: Put the cornstarch in a medium bowl. Whisking steadily, slowly pour in 1/2 cup of the milk, mixing until quite smooth. Whisk in the whole eggs and egg yolks, mixing again until smooth, then gradually whisk in the rest of the milk, the cream, salt, and nutmeg. Use immediately or refrigerate, covered, for up to one day. If using the next day, be sure to re-whisk. Prepare Zucchini Mixture: In a nonstick pan, heat oil over medium heat. Add garlic and shallots and stir until fragrant, about 2 minutes. Add grated zucchini, and stir until just softened, another 3-4 minutes. Remove from heat. Oil mini muffin tins well. Put a pinch grated cheese into each muffin cup, a teaspoon of zucchini mixture, and pinch of chopped fresh basil. Pour 1 tablespoon of the batter into each muffin cup. Bake until the quiches puff and start to turn golden, 15-18 minutes. Let cool for 10 minutes and then carefully run a paring knife around the rim of each muffin cup. Carefully lift each quiche out of its cup. Mini quiches freeze very well. Let cool, then freeze in a single layer in a covered container. Reheat on a cookie sheet in a 400 degree oven for about 5-10 minutes.