Preheat oven or grill to 425ºF (220ºC) and line a baking sheet with parchment or aluminum foil. Place pepper halves cut-side down / skin-side up on the baking sheet. Drizzle with a little olive oil and sprinkle with a pinch of kosher salt. Roast for 35 minutes until the skins are deeply blistered and caramelized.
Melt the butter in a large Dutch oven or soup pot over medium heat. Add the finely chopped yellow onion and sauté for 5–6 minutes until soft. Stir in the tomato paste and cook for 2 minutes until deepened in colour. Add the smoked paprika, stirring constantly for 30 seconds to bloom the spice.
Slice or tear the red pepper halves in half and add them (and any reserved pepper juices) into the pot. Pour in the 5 cups of vegetable broth and add the sprig of fresh rosemary. Season with 1 teaspoon kosher salt and a generous grind of fresh black pepper. Bring the soup to a boil over high heat, then immediately reduce the heat to low. Cover the pot and let it gently simmer for 15 minutes.
Turn off heat, remove rosemary sprig and discard. Using an immersion blender, purée the soup directly in the pot until it's completely smooth and velvety. (If using a standard countertop blender, let the soup cool slightly, blend it in small batches with the lid vented to let steam escape, and pour it back into the pot).
Place the pot back over low heat, stir in the ½ cup of heavy cream, and let it warm through for 1–2 minutes. Taste and season with more salt and pepper as desired. Serve with crusty bread.