Cook the beets in boiling water until soft, about 30 minutes. Peel and let cool. Slice very thin.
Line a bread tin with plastic wrap, leaving enough overhang to be able to fold it over to cover the terrine.
Starting with the lighter coloured beets, layer the beets and goat cheese, as if you were making a lasagna. Do not worry if the layers are uneven. Season with salt and pepper and a small drizzle of olive oil between layers. Finish with the red beets on top, and fold over the plastic wrap to cover the top.
Place a weight on the terrine so it gets compressed. Add a similarly sized bread tin on the top, and place a heavy object inside, such as a can of soup or veggies. Place in the fridge for a minimum of two hours, preferably overnight.
When ready to serve, pull the terrine out of the tin to slice on a board. Unwrap the terrine, and carefully slice about 1/2” thick. Use a spatula to transfer the beet-goat cheese jewels to a serving platter, and sprinkle with coarse sea salt.