In a large pot over medium heat, melt butter and olive oil until shimmering. Add chopped onion and garlic; sauté until translucent, about 5 minutes.

Stir in broccoli and cauliflower florets, coating in the sautéed aromatics. Cook for 3 minutes until veggies glisten and start to soften.

Pour in vegetable broth, season with salt, pepper, and a pinch of nutmeg. Bring to a gentle boil, then simmer covered for 10 minutes until tender.

Remove from heat and transfer soup in batches to a blender, or use an immersion blender, until perfectly silky and velvety.

Return smooth soup to low heat, pour in heavy cream or coconut milk, stirring for 2 minutes without boiling, until heated through.

Taste and adjust salt, pepper, or nutmeg as needed. The soup should be rich, smooth, and gently spiced.

Ladle into bowls, top with grated Parmesan and chopped chives. Enjoy the full comfort of this Creamy Broccoli Cauliflower Soup Recipe.