Set one oven rack to the center position and one to the upper-middle position. Preheat oven to 350º F.
With a paring knife, cut an "x" in the bottom of each Brussels sprout and place all in a large bowl.
Add the vinegar, apples, almonds, salt, ground peppercorns, oil, onions, raisins and pepper flakes. Toss together and transfer to a gratin or baking dish and dot the top with half the butter.
Bake on lower rack for 30 minutes. Sprinkle the remaining butter over the top, return to the oven and bake for another 30 minutes.
Remove dish from oven and turn on the broiler. Place the baking dish on the upper-middle rack and broil for 2 minutes, or until the top of the casserole is browned. Watch this carefully, making sure the casserole doesn't burn.
This is delicious served hot or at room temperature.