In a large skillet melt the butter over medium heat. Add the mushrooms, scallions, and peppers, season with salt and pepper, and sauté for about 8 minutes until tender and any liquid the mushrooms have released evaporates. Stir in the parsley, and transfer the vegetables into a large mixing bowl.
Add the cream, provolone, mozzarella, Parmesan, eggs and Sriracha sauce and stir well to combine. Add the ham and stir until evenly mixed together.
Take the pie crust out of the fridge 15 minutes before using. Unroll the slightly softened dough, and with the help of the parchment paper, flip it into a 9-inch pie pan. Remove the paper and gently press the dough to fit against the bottom and sides of the pan. Trim and flute the edges as desired.
Brush the inside of the pie crust with the mustard. Scrape the filling into the pie pan and smooth the top. Bake for 35 to 45 minutes until a the top is browned, and knife inserted into the center of the pie comes out clean. Transfer the pie to a cooling rack and cool until warm or room temperature. Cut into wedges and serve.