Meanwhile, slice each onion half into 4 or 5 segments. In a heavy skillet, melt half the butter over medium-low heat. Cook onions, stirring occasionally, for about 20 minutes or until softened, reducing heat to low if browning too quickly.
Add remaining butter to potatoes in pot and, using a potato masher, mash thoroughly. Mash in milk. Using a wooden spoon, stir potatoes briskly, incorporating a little air into the mash.
Spoon half the potatoes into prepared baking dish, smoothing surface. Layer cooked onions evenly overtop. Season to taste with freshly ground pepper. Sprinkle Stilton evenly overtop. Spoon in remaining mashed potatoes, smoothing lightly with the back of a large spoon or spatula. Sprinkle evenly with Parmesan.
Bake for 30 minutes or until top is golden and edges are bubbling. Remove from oven and let stand on wire rack for 5 minutes before serving.