Melt butter in a large pot over medium heat until lightly foaming.
Add minced garlic; sauté ~60 seconds, stirring constantly.
Whisk in flour; cook ~2 minutes until light golden and nutty.
Slowly whisk in chicken broth; bring to a gentle simmer.
Simmer 5–7 minutes, stirring occasionally, until slightly thickened.
Reduce heat to low; pour in heavy cream and warm ~3 minutes (don’t boil).
Remove pot from heat for 2 minutes to cool slightly.
Stir in Parmesan in three batches; melt fully between additions.
Adjust with salt and pepper; thin with a splash of broth/cream if needed.
Ladle into bowls; top with herbs, croutons, and Parmesan shavings.