Preheat the oven to 375 degrees.
In a medium skillet, heat the oil over a medium high heat. When the oil is hot, add the mushrooms and sauté, stirring occasionally, until all the moisture has been released and the mushrooms have turned dark brown, about 10 – 15 minutes.
Meanwhile, in a 9-inch pie pan, combine the flour, melted butter, ½ tsp. salt, and 2 Tbsp. milk and mix well with a fork. Then, using your hands, finish mixing, if necessary, and then press the dough into pan to form a crust.
In a small bowl, steam the broccoli in the microwave for 3 - 4 minutes, or until soft. Then put the broccoli on the counter and chop it finely.
In a large bowl, combine the mushrooms, 1 ¼ cups milk, broccoli, eggs, cheese, ¼ tsp. salt, and black pepper and stir well.
Pour the egg mixture into the pie pan and bake for 30 – 40 minutes, until the filling is set in the middle (and prepare the salad, if you are serving it). Serve immediately, refrigerate for up to 3 days, or freeze for up to 3 months.