Preheat the oven to 325 degrees. Wrap beets in tin foil and place on a baking dish. Pour 1/4 cup of water into the foil. Roast until beets are fork tender, 1 to 1 1/2 hours, depending on the size of the beets. Set aside to cool.
Make the vinaigrette: In a medium bowl, whisk together the minced shallot, white wine vinegar and honey. Slowly whisk in the olive oil. Season with salt and pepper to taste and set aside.
When beets are cool enough to handle, rub the skins off with your fingers. They should slip off easily. Using a mandolin or sharp chef’s knife, slice the beets into very thin rounds. Layer slices on a platter, drizzle with vinaigrette and top with torn basil.