Cook the beets in a large pot of water until they are fork-tender, about 45 to 60 minutes. Drain and cool. Once cool enough to handle, peel the beets and slice them into thin, even rounds using a sharp knife or a mandoline.
In a medium mixing bowl, combine the goat cheese, garlic, goat feta, olive oil, thyme, and black pepper. Mix with a fork or spatula until smooth and spreadable. Add more oil if necessary to loosen the texture.
In a food processor, combine the parsley leaves, garlic cloves, olive oil, almond flour, salt, and black pepper. Process until you get a smooth, green paste. Scrape down the sides as needed for even blending.
Line the bottom of a 20 cm/8-inch springform pan with a layer of beet slices, slightly overlapping them to cover the surface completely. Spread half of the cheese mixture evenly over the beet layer using a small offset spatula or the back of a spoon. Add a second layer of beet slices, then spread the green herb paste evenly on top. Add a third layer of beet slices, followed by the remaining cheese mixture. Finish with a final layer of beet slices, pressing down gently to compact the terrine.
Drizzle a little olive oil over the top and smooth the surface. Cover the terrine tightly with plastic wrap or foil and refrigerate for at least 3 hours, or overnight, until set and chilled through.
To serve, carefully remove the terrine from the springform pan and transfer it to a serving plate. Sprinkle the top with chopped walnuts and fresh thyme just before slicing.