Preheat oven to 425°F.
Brush roast with oil. In a small bowl, combine 2 tablespoons minced onions, 1 tablespoon salt, the thyme, mushroom powder and granulated garlic. Rub mixture into roast.
Place roast on a wire rack inside a shallow pan. Insert an ovenproof meat thermometer horizontally in the thickest part of the roast. Roast for 15 minutes. Reduce heat to 275°F and cook for 2 hours or until the thermometer registers 135°F for medium-rare, 145°F for medium, and 150°F for medium-well. (See tip)
Remove roast from oven and tent with foil. Let stand 15 minutes.
Pour beef juices from the roasting pan into a 4-cup measuring cup. Add beef broth and enough water to measure 3-½ cups. In a medium saucepan over medium-high heat, add the liquids, remaining dried onions, the Worcestershire sauce and sugar. Bring mixture to a boil. Reduce heat and simmer, stirring often, 5 minutes. Season to taste with pepper and more salt (if needed). Strain the mixture into small serving bowls. Keep warm.
Carve the meat against the grain and arrange on a serving platter. Ladle some of the juices (au jus) over the beef slices.
Serve carved rump roast with the remaining au jus alongside.