In a skillet, melt butter over medium heat. Add onion and sugar; cook, stirring for 10 minutes or until softening. Continue to cook, stirring often for about 10 minutes or until very soft and golden. Stir in balsamic and thyme and cook for 2 minutes; remove from heat.
In a small bowl, whisk together sour cream, mayonnaise, horseradish and pepper. In a saucepan, bring beef broth to a gentle simmer. Add roast beef to heat through.
Spread bottom of slider buns with Horseradish cream. Divide onions among bottom buns. Using tongs, remove roast beef from broth letting drain and add to sliders. Stir in Worcestershire sauce and garlic into broth; let simmer for 2 minutes.
Meanwhile, top beef with cheese and top each slider with top bun. Place sliders on a baking sheet if desired to warm through in a 400 F (200 C) oven for about 5 minutes. When ready serve with broth mixture to dip sliders into.
Top 5 Nutrients: Iron 22%DV, Calcium 17%DV, Vitamin A 11%DV, Vitamin C 5%DV, Vitamin B6 5%DV, Folate 3%DV.