Look for cooked and peeled beets in the produce section of your supermarket.
In a large bowl combine the beef, 1/4 teaspoon salt, and pepper to taste. Shape beef into 8 patties. Heat a grill pan over medium-high heat. Grease with 1 teaspoon olive oil. Cook patties 3 to 4 minutes per side or until done (160°F). Place patties on slider buns and top with arugula.
In a medium bowl, combine the beets, balsamic vinegar, 2 teaspoons olive oil, a pinch of salt and pepper to taste. Top with goat cheese and serve with the sliders.