Slice the beets into ½ cm disks. Place them in a flat dish, then drizzle with oil and vinegar. Leave to marinate for an hour.
Meanwhile, mix the goat cheese with the milk and chives until creamy.
Drain the beet disks (but keep the marinade) and wipe them with a paper towel.
Put a beet slice on a serving plate, add a scoop of goat cheese then press another disk on top to even out the cheese. Keep doing this until you've got 4-5 layers. The top should be a beet slice. Then using a knife or spatula remove the excess cheese from the sides.
Scatter salad leaves and walnut around the tartlets and drizzle with the marinade.