Preheat the oven to 225 degrees Celsius / 435 Fahrenheit with top and bottom heat.
Cut the tomatoes, potato, and bell peppers into large chunks. Grate the carrot and slice it. Peel the garlic cloves and shallot and cut them into large chunks.
Spread the vegetables on a baking sheet and drizzle with olive oil, paprika, pepper, and salt to taste.
Roast the vegetables in the oven for 30 minutes. Stir halfway through.
Heat olive oil in a large soup pot and briefly fry the tomato purée.
Add the grilled vegetables, along with water and a bouillon cube. Bring to a boil, then simmer for 5 to 10 minutes.
Puree the soup until smooth using an immersion blender, then stir in two tablespoons of Boursin. Taste the soup and season with salt, pepper, and additional Boursin, if desired.
Divide the soup between four bowls, garnish with a spoonful of Boursin and fresh herbs, and enjoy! Tip: It's delicious with homemade bruschetta on the side.