Preheat the oven to 425ºF. Line a baking sheet with parchment paper. Combine the first 7 ingredients in a bowl, and then spread vegetables on the baking sheet. Roast 30 minutes, stirring once, or until tender and nicely coloured. Cool vegetables to room temperature.
Now heat oven to 375ºF. Place eggs in a bowl and beat well. Mix in milk, provolone cheese, basil, salt and pepper. Stir in the roasted vegetables. Thoroughly coat a 9-inch non-stick pie plate with vegetable oil spray. Pour egg mixture into the pie plate.
Pull goat cheese into small nuggets and set on top of the quiche. Bake 20 to 25 minutes, or until the quiche is set. Let quiche rest at least 10 minutes before slicing and serving.
Note: To ensure the wedges of quiche come out clean, use a good quality (no scratches) non-stick pie plate. Diced in this recipe means to cut into ¼” cubes. Herb-flavoured goat cheese is available in the deli department.