Heat a large pot or Dutch oven over medium heat. Add the butter, olive oil, onion, and ¼ teaspoon salt. Cook until the onions begin to soften, about 3 minutes, stirring occasionally.
Add the garlic and paprika. Cook until fragrant, about 1 minute, stirring frequently.
Add the tomato paste and cook for 1 minute, stirring frequently.
Add the roasted red peppers, diced tomatoes, stock, water, and remaining 1¼ teaspoon salt, stirring to combine.
Cover, bring to a boil, then reduce to a simmer. Simmer, covered, for 15 minutes, stirring occasionally.
Uncover and turn off the heat. Using an immersion blender, carefully blend until smooth. Alternatively, working in batches, ladle carefully ladle into a blender. Blend until smooth.
Add the cream and sugar, stirring until the sugar has dissolved. Taste and add additional salt if desired.
Top with goat cheese, parsley, and red chili flakes, if using.