Place the asparagus in a single layer on a large platter. Drizzle with 1 tablespoon of oil and black pepper. Toss to coat.
Heat the grill to medium. Place a multi-funtional perforated grill pan on the grill. Place the asparagus on the pan in a single layer and grill for 8 minutes or until the asparagus is tender-crisp, turning halfway through cooking. Remove from heat to a cutting board and let cool.
Heat the remaining oil in a 4-quart saucepan over medium heat. Add the onion and garlic and cook until tender-crisp.
Meanwhile, cut the grilled asparagus diagonally into 1-inch pieces. Set aside.
Reduce the heat to low. Add the flour to the onion mixture. Cook for 5 minutes, stirring often. Gradually stir in the broth. Heat to a boil. Reduce the heat to low. Cover and cook for 10 minutes.
Place 1/3 of the broth mixture into an electric blender or food processor container. Cover and blend until smooth. Pour the mixture into a medium bowl. Repeat the blending process twice more with the remaining broth mixture. Return all of the purÈed mixture to the saucepan. Add the remaining asparagus and rosemary. Cook over medium heat until the mixture is hot. Garnish with rosemary sprigs, if desired.
Tip: Heat a ridged grill pan over medium heat. Place the asparagus on the pan. Cook for about 8 minutes or until tender-crisp, turning the asparagus spears over with kitchen tongs halfway through cooking.
Creamy Grilled Asparagus Soup: Add 1/2 cup half-and-half or heavy cream when reheating soup in step 5.