Preheat oven to 450°F. Add the pie crust to a 9-inch pie pan and flute the edges. Poke the bottom of the crust with a fork, and refrigerate until ready to use.
In a skillet, sauté the mushrooms, broccoli and onion in the butter until the onion is tender and the vegetables have released their liquid; drain.
In a bowl, whisk together the milk, light cream and eggs until blended. Stir in the lobster and sautéed vegetables. Add the dry mustard, basil, salt and pepper and mix well.
Pour the lobster mixture into the pie crust. Bake for 10 minutes. Reduce the oven temperature to 325°F. and bake for 20 to 30 minutes longer or just until the center is firm.
Notes
Another idea... serve with a tossed green salad for a light summer dinner.