Place the beets and pickling spices in a large saucepan filled with just enough water to cover. Add vinegar or lemon juice to prevent beets from "bleeding." Bring to a boil, reduce heat and simmer until tender (about 45-60 minutes). Rinse beets immediately under cold water. Peel the beets when they are cool enough to handle. Use a cookie cutter or other circle form to cut beet circles to fit the buns, each about 1.5 inches thick.
Spread bottom half of each bun with a generous amount of chimichurri. Top with a beet slice and spread more chimichurri on top of the beet. Top with arugula.
Stick a toothpick into each slider to secure the ingredients in place
Note: This offers a hearty tasting sandwich for vegetarians or others who want a break from meat and cholesterol.