Cook whole beets, untrimmed in boiling water with juice of 1 lemon (put the lemon halves in water after squeezing out juice), until tender, about 45 minutes.
Drain, cool and then peel. Slice beets as thinly as possible and set aside.
Beat goat cheese with whipping cream until smooth. Add remaining ingredients, season to taste and fill a piping bag with a large, plain tip.
To assemble, line 6 muffin tin cups or 4-oz ramekins with plastic wrap. Place a single beet slice in the bottom of each cup.
Line sides of each cup with beets, bedding to fit into the edge if needed, so that each cup is entirely lined with beets. Pipe goat cheese filling into each and top with beet slices to cover goat cheese.
Chill for at least 2 hours.
To serve, gently pull out each terrine, unwrap and turn out onto serving plate.
Terrines can be served on a bed of baby greens and a little cucumber with a simple vinaigrette.
Alternately, terrines can have an added layer or smoked salmon or cooked shrimp inside or on top (for a lunch entrée)