Preheat oven to 350°F. Grease a 9-inch quiche or pie pan. Bring 1 inch water to a boil in a skillet. Add asparagus and cook until crisp-tender, 2 to 3 minutes. Drain and rinse with cold water, then pat dry; set skillet aside. Arrange asparagus in prepared pan in a circular pattern. Sprinkle cheese on top.
Melt butter in same skillet over medium heat; add shallot and cook, stirring, until softened, about 5 minutes. Transfer shallot to a bowl; add eggs, half-and-half, salt and pepper; and blend with a fork. Pour over asparagus and cheese.
Bake omelet until puffed and golden, about 40 minutes. Cut into wedges; serve.
I made this a few years ago for a mother's day brunch. It was so simple and elegant and absolutely delicious! I have made it several times since then. Although, there really is no need to mess with perfection, I thought about adding some crispy bacon to it, which I'm sure would make it even more amazing! Time was short that day and it is so perfect on its own. Perhaps the next time I will add some bacon.
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