Combine beet, apple, and ginger with about 1 cup of water in a blender and pulse until blended and smooth. Scoop 2 ounces of beet/apple puree into the bottom of four small cocktail glasses and combine with 1/2 teaspoon honey in each glass. Fill glasses to the top with ice cubes then add 2 ounces of gin and top with 4 ounces of soda water each. Stir well and serve with 2 sprigs of thyme in each glass.