In a large saucepan or Dutch oven, cook the green onions in hot olive oil over medium heat for about 2 minutes, until softened and fragrant. Carefully pour in 4 cups (960 ml) of the vegetable broth, increase the heat, and bring to a boil.
Add the cauliflower florets, return to a boil, then reduce the heat to a simmer.
Cook, uncovered, for 6 to 8 minutes until the cauliflower is just fork-tender.
In a small bowl, whisk together the all-purpose flour and the remaining 1 cup (240 ml) of cold vegetable broth until smooth, creating a slurry. Slowly pour the slurry into the simmering soup, whisking constantly to prevent lumps.
Continue to cook and stir until the soup has slightly thickened and is bubbly, about 2-3 minutes.
Remove the saucepan from the heat to prevent the cheese from separating. Gradually stir in the shredded cheddar and American cheese, a handful at a time, until completely melted and the soup is smooth.
Finish by stirring in the fresh chervil or parsley, salt, nutmeg, and black pepper.
Taste and adjust seasoning if needed before serving warm.
When making the flour slurry, always use cold or room temperature broth.
Whisking flour into hot liquid is a sure way to create lumps.