Core and quarter the tomatoes and scoop out the seeds, reserving the seeds and cores for the stock.
In a large bowl, toss the tomatoes with the garlic, onion, honey, rosemary, 1 tablespoon of the vinegar, 3 tablespoons of the olive oil, and a dash of salt.
Spread the mixture on a baking sheet and roast for 40 minutes, stirring occasionally.
Remove the rosemary and set aside.
Combine the tomato scraps, bay leaf, and 1 cup water in a pot and bring to a boil over high heat.
Decrease the heat and simmer, uncovered, for 15 minutes.
Strain the stock into a bowl and discard the solids.
Rinse the pot and return the stock to the pot.
Add the roasted tomatoes.
Bring to a boil over high heat, then decrease the heat and simmer, uncovered, for 5 minutes.
Let the soup cool for 10 minutes, then pour into a blender.
Add the cheese and blend until smooth.
With the blender running, add the remaining 1 tablespoon olive oil.
Season to taste with salt.
Garnish the soup with the remaining 1 tablespoon balsamic vinegar and a few grinds of pepper and serve.