Prep the broccoli: Cut florets into bite-size pieces. Peel and dice the stems; they’re great in soup and add extra fiber.

Sauté aromatics: In a large pot, heat butter and olive oil over medium. Add onion with a pinch of salt and cook 3–4 minutes until translucent. Stir in garlic for 30 seconds until fragrant.

Add broccoli and broth: Toss in broccoli florets and stems. Pour in the broth and bring to a gentle boil. Reduce to a simmer and cook 8–10 minutes, until broccoli is tender but still bright.

Blend partially: Use an immersion blender to blend about half the soup, leaving some chunks for texture. If using a countertop blender, work in small batches and vent the lid. Return blended soup to the pot.

Stir in cream and seasonings: Lower heat to medium-low. Add heavy cream, mustard or Dijon, smoked paprika, and a few grinds of black pepper. Simmer 2–3 minutes—do not boil.

Melt the cheeses: Reduce heat to low. Add cream cheese (if using) and whisk until smooth. Slowly sprinkle in cheddar by the handful, stirring constantly until fully melted and silky. Do not boil after adding cheese to prevent graininess.

Taste and adjust: Season with salt to taste. Add a pinch of red pepper flakes for gentle heat and a splash of lemon juice to brighten, if you like.

Serve: Ladle into bowls and top with a little extra grated cheddar or a grind of black pepper. Enjoy warm.