Begin by finely dicing a medium onion and mincing two cloves of garlic.
Heat a heavy-bottomed pot over medium heat and add a tablespoon of butter or olive oil. Once shimmering, add the diced onion.
Sauté the onion for about 5-7 minutes until it becomes translucent and fragrant, with some golden edges forming.
Add the minced garlic to the pot and cook for about 30 seconds, stirring constantly until fragrant but not browned.
Stir in the fresh broccoli florets, coating them in the aromatic mixture. Cook for 3-4 minutes until the broccoli turns bright green and starts to soften slightly.
Pour in the broth, bringing the mixture to a gentle simmer. Cover and cook for 10-12 minutes until the broccoli is tender but not mushy.
Stir in the shredded cheddar cheese gradually, stirring until melted and smooth, creating a cheesy, velvety base.
Use an immersion blender directly in the pot or carefully transfer the soup in batches to a blender. Puree until smooth and velvety, then return to the pot.
Stir in the cream or milk, along with a pinch of nutmeg, salt, and black pepper to taste. Warm gently until steaming and slightly thickened.
Taste the soup and adjust the seasoning as needed, adding more salt, pepper, or lemon juice to brighten flavors.
Serve the hot broccoli cheddar soup in bowls, garnished with extra cheese or a drizzle of cream if desired, and enjoy its creamy, comforting texture.