Preheat the oven to 400 degrees F.

On a sheet pan, gently toss together the tomatoes, peppers, onion, garlic, thyme, 2 tablespoons olive oil, vinegar, and salt and pepper to taste. Arrange the tomatoes and red peppers, skin side up, and bake until lightly charred, 45 to 50 minutes.

In a soup pot, warm the remaining 2 tablespoons of the olive oil over medium-high heat. Stir in the tomato paste and mix well. Add the tomato and pepper mixture, including the juices, and combine. Stir in the stock, cover, and bring to a boil. Reduce the heat to low and simmer for 20 minutes. Transfer the soup to a blender* (or use an immersion blender) and pulse in small batches that reach only about a third to halfway up the side of the jar. Be careful to start slow then increase the speed to blitz the ingredients until smooth. Use a separate bowl to hold the blended soup and then return it all to the pot.

Heat the soup to warm through, then ladle into serving bowls and garnish with basil.

*When blending hot liquids: Remove liquid from the heat and allow to cool for at least 5 minutes. Transfer liquid to a blender or food processor and fill it no more than halfway. If using a blender, release one corner of the lid. This prevents the vacuum effect that creates heat explosions. Place a towel over the top of the machine, pulse a few times then process on high speed until smooth.