Cut off any rough ends of the asparagus. Slice good parts into 2 inch pieces.
In a large pot, heat asparagus, broth, onion, garlic, and 1/2 teaspoon thyme over medium-high heat. Let boil, then lower heat to medium-low, place lid on pot, and simmer for 10 minutes. Take pot off heat and let rest for 10 minutes.
Using a food processor or blender, pulse asparagus mixture in portions until creamy. Pour back into pot when done.
Combine flour and milk, stirring until lump free. Slowly pour flour mixture into asparagus mixture stirring until fully combined. Let boil, stirring continually. Lower heat and cook for 5 more minutes, stirring continually.
Take pot off of heat and mix in butter, salt, 1/4 teaspoon lemon rind and the rest of the thyme. Take pot off of heat and mix in butter, salt, 1/4 teaspoon lemon rind and the rest of the thyme.