In a medium pot, melt the 3 tablespoons butter over medium-high heat. Add the onions, salt, pepper, and nutmeg and cook, stirring, until soft, 3 minutes. Add the garlic and thyme cook, stirring, until fragrant, for 20 seconds. Add the flour and cook, stirring until the mixture is well blended and smells fragrant, 2 minutes. Slowly add the chicken stock, whisking constantly, and bring to a boil. Reduce the heat and simmer until thickened, about 5 minutes. Add the broccoli and cook, stirring, until tender, for 10 minutes.
Remove the pot from the heat and puree with a hand-held immersion blender. (Alternatively, in batches, puree in a blender or food processor and return to the pot.)
Add the cream and bring to bare simmer to heat through. Add the cheese and cook over low heat, stirring, until melted. Add the remaining 2 tablespoons cold butter, stirring to blend.
Remove from the heat and ladle the soup into bowls. Sprinkle croutons over the top of the soup and serve immediately.
Preheat the oven to 400 degrees F.
Place the bread in a medium bowl and toss with oil and Essence. Spread evenly on a small baking sheet and bake, stirring twice, until light golden brown on top, about 6 minutes. Remove from the oven and cool slightly before serving.
Emeril's ESSENCE Creole Seasoning (also referred to as Bayou Blast):
Combine all ingredients thoroughly.
Recipe from "New New Orleans Cooking", by Emeril Lagasse and Jessie Tirsch. Published by William and Morrow, 1993.