Step 1Bring the asparagus peels and water to a boil in a 4-quart saucepot. Reduce the heat to a simmer and cook the peels about 20 minutes, then strain, reserving the broth.
Step 2Heat the butter in a medium saucepan over medium heat until melted. Stir in the onion and cook until tender, but not browned, about 2 minutes. Stir in the flour. Cook and stir until blended and smooth, about 1 minute.
Step 3Stir in 5 cups of the asparagus peel broth. Bring to a boil. Reduce the heat and simmer 5 minutes. Stir in the cream and white pepper to taste. Simmer 1 minute.
Step 4To serve, cut the asparagus spears into 1-inch slices and put a few slices in the bottom of each bowl. Divide the soup among the bowls and serve.