Preheat the oven to 400°F (200°C). Wash the beetroot and wrap each one in foil. Place them on a baking tray and roast for 45–60 minutes, depending on their size, until a knife slides easily into the center. Alternatively, boil them until tender.
Let the cooked beetroot cool enough to handle. Rub off the skins, trim the ends, and pat the beets dry. Slice them into thin, even rounds, about ⅛ inch thick. Keep the slices as uniform as possible for neat layers.
Place the goat cheese in a bowl with the cream or Greek yogurt, olive oil, lemon juice, chives, thyme, salt, and black pepper. Mix until smooth and spreadable. If the cheese is very firm, add a little extra cream or yogurt.
Line an 8 × 4-inch loaf pan with plastic wrap, leaving enough overhang on the sides to cover the top later. Make sure the lining fits into the corners so the terrine is easier to remove.
Arrange a layer of beetroot slices across the bottom of the mold, overlapping them slightly. Spread a thin layer of goat cheese mixture over the beetroot. Continue alternating the beetroot and cheese until all the ingredients are used, finishing with a layer of beetroot.
Fold the plastic wrap over the top. Place a small, flat weight on top if desired, using gentle pressure to help the layers hold together. Refrigerate for at least 4 hours, or overnight, until firm.
Open the plastic wrap and turn the terrine onto a serving plate. Carefully remove the mold and peel away the remaining wrap. Use a sharp knife to cut clean slices, wiping the blade between cuts.
Finish with a few fresh thyme leaves or chopped chives and a light drizzle of olive oil. Serve chilled with toasted bread, crackers, or a fresh green salad.
