Scrub, rinse and pat beets dry then rub with a small amount of olive oil and wrap tightly in foil (two beets per foil packet). Roast for 1 to 1 1/2 hours until beets are tender and easily pierced with a knife. Allow to slightly cool then carefully remove skin. (The beets will stain your hands and clothing! So I use rubber gloves.) Set aside.
In a small, dry frying pan toast walnuts until slightly browned. Set aside.
In a small owl, whisk together balsamic vinegar and walnut oil then season with salt and pepper to taste. Set aside.
Once skin is removed slice beets width-wise into three or four sections (depending on the size of the beet.)
In layers, alternate beet slices and crumbled goat cheese. Drizzle stacks with balsamic walnut oil vinaigrette, fresh thyme leaves and the toasted walnuts.