Preheat oven to 300°F (150°C). Brush both sides of ribs with 1 tbsp (15 mL) olive oil. Sprinkle with ½ tsp (2 mL) each salt and pepper. Wrap ribs in foil and place on large baking sheet. Bake 2 hr., or until a meat thermometer registers 160°F (71°C).
Meanwhile, combine root beer, barbecue sauce and molasses in medium saucepan over medium heat. Bring to a boil; immediately reduce heat to low and simmer 30 min. or until sauce is thickened and coats back of spoon.
In bowl, mix remaining 2 tbsp (30 mL) olive oil, vinegar, mustard, and remaining ¼ tsp (1 mL) each salt and pepper. Brush 2 tbsp (30 mL) of mixture onto leeks. Add carrots and dill to remaining oil mixture in bowl; toss to coat. Set vegetables aside.
Remove ribs from foil and brush with 2 tbsp (30 mL) of the root beer sauce. Grill ribs and leeks about 5 min. on barbecue preheated to medium-high. Brush ribs occasionally with additional root beer sauce. Grill leeks, turning occasionally, until softened. Cool ribs slightly before slicing apart; serve with remaining root beer sauce for dipping, and grilled leeks and carrot slaw on the side.
Root beer can be substituted with an equal amount of cola.