Slice acorn squash into rounds about 1 inch thick. Slice butternut squash into about 1-inch chunks. Slice kabocha squash into half-moon slices, also about 1 inch thick. Spread the squash out onto a sheet tray, making sure they are in a single layer and slightly spaced out; use two sheet trays if necessary. Drizzle all the squash with the honey and half the olive oil, season with salt and pepper and roast until soft but not falling apart, 15 to 20 minutes.
Core Brussels sprouts and cut into quarters. Spread them out on a sheet pan, drizzle with remaining olive oil and season with salt and pepper. Roast until slightly tender, 10 to 15 minutes.
Spread pepitas out on a sheet tray. Sprinkle with salt and lightly toast until they pop and are a light brown, 6 to 10 minutes.
In a small bowl, whisk together the pumpkin seed oil and lemon juice. Lightly dress the arugula leaves with the mixture.
To assemble, place dressed arugula on a large platter, then arrange squash and Brussels over the arugula. Sprinkle with pepitas and pomegranate seeds and garnish with shaved Parmesan.