Can i substitute parchment paper for foil when roasting beets?

make a salt pack with kosher salt and a few egg whites

Using aluminum foil creates a "steam" pocket. You will lose that with the parchment paper. Maybe parchment paper as a liner then an inversed stainless steel bowl to create a steam chamber?

We always called parchment paper in the UK, grease-proof paper. We would rub butter or oil on one side and it did almost everything foil would do. . . . so try rubbing it with oil and place on a sheet pan for roasting

Parchment paper is somewhat porous. So you'll probably have some leakage. But I think it should work. Like "en papillote". Place on a sheet pan to catch any leaks.