Wrap the beets in a square of tin foil. Place on a sheet tray and roast until tender, 30 to 35 minutes. Once cool enough to handle, peel the skins of the beets. Slice into 1/4-inch-thick slices using a mandoline. (Use a sharp chef's knife if you don't have a mandoline.)
Add the lemon juice to a small bowl along with the parsley and season with salt and pepper. Drizzle in the olive oil while whisking.
Lay the beets on platter and drizzle with the vinaigrette. Sprinkle with the pistachios or serve them on the side for some salty crunch.