Preheat the oven to 300˚F (150˚C). Line a baking sheet with parchment paper.
In a large bowl, toss together the olive oil, tomatoes, onion, garlic, Savory spice blend, salt, and pepper.
Place the tomatoes cut-side down on the prepared baking sheet and spread the onions and garlic around the pan in a single layer.
Roast for 40 minutes, until the tomatoes have wrinkled. Leave the oven on for making the grilled cheeses.
In a large pot over medium-high heat, combine the roasted vegetables, vegetable stock, and rice. Bring to a boil, then cover, reduce the heat to low, and simmer for 20 minutes, until the rice is tender. Add the diced tomatoes and balsamic vinegar and stir to combine. Remove the pot from the heat.
Blend the soup with an immersion blender until completely smooth and creamy.
Ladle into bowls and top with basil.