Heat olive oil in a Dutch oven over medium heat until shimmering. Add onion, red bell peppers, salt, and pepper. Cook, stirring occasionally, until softened and lightly browned, about 6 to 8 minutes.
Stir in garlic, dried mint, smoked paprika, and red pepper flakes. Cook until fragrant, about 30 seconds. Stir in tomato paste and cook for 1 minute.
Stir in white wine, scraping up any browned bits from the pot. Cook until reduced by half, about 1 minute. Add fire-roasted tomatoes and their juices, stirring occasionally. Let cook until the tomatoes soften and begin to break apart, about 10 minutes.
Stir in chicken or vegetable broth, water, and rinsed bulgur. Bring the mixture to a simmer, then reduce heat to low. Cover and cook gently until the bulgur is tender, about 20 minutes. Adjust seasoning with additional salt and pepper, if needed.
Sprinkle the soup with freshly chopped mint before serving. Enjoy as a hearty standalone dish or pair with crusty bread for a complete meal.