In a food processor blend avocados after you have discarded pits and skins. Add apple cider vinegar, pinch salt and tarragon. Blend until smooth. Scrape down sides of food processor once or twice during that process.
Turn on food processor and SLOWLY drizzle olive oil into running processor. The mixture will thicken. Blend for a minute or two and scrape down sides if needed with spatula.
Wash dirt off of beets. Pat dry. Carefully slice raw beets as thinly as possible. Use a hand mandolin if you have one.
Arrange beet slices on a plate and put a spoonful of tarragon olive oil mayonnaise on top.
Decorate with a bit of fresh tarragon and drizzle plate with olive oil. Don’t forget the drizzle of olive oil; it really enhances the overall flavor of the dish.