While squash is cooking, cut eggplant into small triangle pieces. I did this by slicing ¼-1/2" thick slices, then quartering the slices.
Place eggplant slices on a baking sheet and season with salt. Let sit for 30 minutes to let the eggplant "sweat."
After 30 minutes, there will be some condensation on the eggplant. Dab dry with paper towel.
Drizzle eggplant with olive oil, making sure it is well distributed among the pieces.
Once butternut squash is done roasting, turn oven's broiler on.
Place eggplant on baking sheet under broiler and broil until golden. In my oven, this took about 5 minutes, but watch yours carefully so it does not burn.
Remove from oven and let cool.