Dice the sweet onion into 1/2-inch pieces, cut carrots into 1/4-inch rounds, cut broccoli florets into 1-inch pieces, strip thyme leaves from stems, finely chop fresh sage, and grate the nutmeg fresh. Heat the salted butter and extra virgin olive oil together in a large pot over medium heat until the butter is melted and foaming. This combination of butter and oil gives you the richness of butter with the higher smoke point of oil, preventing burning while building a flavorful base.
Add the diced onion to the hot fat and cook for 3-5 minutes, stirring occasionally, until softened and beginning to turn translucent. Add the carrots and thyme, then season generously with kosher salt and black pepper. Cook for another 5 minutes, allowing the carrots to begin softening and the thyme to release its oils into the fat. This layering of aromatics creates a deeper flavor foundation than adding everything at once.
Pour in the vegetable broth, then add the broccoli florets, bay leaves, grated nutmeg, and cayenne pepper. Bring to a boil, then reduce heat, cover, and simmer for 10-15 minutes until the broccoli is completely tender and falls apart easily when pressed with a spoon. Remove the bay leaves before moving to the next step. I find that cooking the broccoli fully here ensures it blends smoothly and creates a naturally creamy texture without needing heavy cream.
While the soup simmers, whisk together the all-purpose flour, baking powder, kosher salt, and black pepper in a medium bowl. Create a well in the center and add the room-temperature buttermilk, grated Parmesan cheese, and chopped sage. Stir until just combined into a thick, slightly sticky batter—do not overmix, as this keeps the dumplings tender. The batter should be wetter than biscuit dough but thicker than pancake batter.
Using an immersion blender, blend approximately 3/4 of the cooked soup directly in the pot until the broccoli is finely chopped and the soup reaches a creamy, chowder-like consistency. Leave some broccoli pieces visible for texture—this isn't a smooth puree. If you prefer a completely smooth soup, blend it all, but I like to keep some texture to remind you this is a vegetable soup, not a cream soup.
Bring the blended soup back to a gentle boil over medium heat. Using two spoons or a small cookie scoop, drop roughly 6 dumplings into the simmering soup, spacing them apart so they have room to expand. Reduce heat to medium-low, cover the pot, and cook for 8-10 minutes until the dumplings are puffed and cooked through. The dumplings will float to the surface when done.
Gently move the cooked dumplings to the side of the pot. Reduce heat to low, then stir in the whole milk and freshly shredded sharp cheddar cheese, stirring constantly until the cheese melts completely and the soup is smooth and creamy. Taste and adjust seasoning with additional kosher salt and black pepper as needed. I prefer freshly shredded cheddar here because pre-shredded cheese contains anti-caking agents that can make the soup grainy—the real cheese melts silkier.
Ladle the hot soup into bowls, ensuring each serving gets a dumpling or two. Finish with a crack of fresh black pepper if desired.