In a large pot of lightly salted boiling water, blanch beet stems until tender. With a slotted spoon or spider strainer, remove from water and place in a colander. Gently press out water with the back of a large spoon, the spider strainer, or if cool enough, squeeze in your hands. Place stems in a dish.
Add beet leaves to boiling water and blanch until tender. Remove from water, cool slightly in colander, and squeeze out excess water again. Roughly chop the beet leaves. Place them in the dish with the stems and salt these very well.
In a pan, heat olive oil. Add garlic and cook until just barely golden. Add beet greens and sauté for 5 minutes. Taste for salt, and add more if desired.
Whisk together the eggs, ¼ teaspoon salt, a grating of pepper, the cream, and the tarragon.
Heat a small 8" cast-iron frying pan or non-stick pan over medium heat. Add a slick of olive oil to pan to coat bottom. Pour in egg mixture and sprinkle beet greens over top. With a rubber spatula, gently lift edges of the frittata and let the uncooked egg run underneath.
Sprinkle on the goat cheese. Continue lifting the edges, until almost done, and bottom of frittata is golden.
Carefully invert a dinner plate over the pan, hold tight, grab the hot handle with a dry dish towel and flip upside down. Your frittata should now be upside-down on the plate. If pan is dry, add just a touch of olive oil to the pan. Next, slide the frittata back in the pan and continue cooking until done and bottom is golden. Alternatively, to avoid the fliperoo, place the frittata under the broiler for a few minutes until done.
Turn out onto a serving dish. Cool slightly. Garnish with additional fresh tarragon, and scoops of goat cheese drizzled with olive oil sprinkled with sea salt. Cut into wedges, or 1" hors d'oeuvre-sized squares, and serve. Frittatas are great warm, room temperature, or cold.