Heat olive oil in pan. Add the onion, and cook until it’s golden and wilted, about 10 minutes.
Add tomatoes, chili, and rosemary. Stir occasionally and cook for 30 minutes until sweet and caramelized.
Deglaze the pan with the vermouth, and stir until combined.
Pour the honey over the tomatoes and toss to combine.
Serve with warm bread, sliced Asiago, and rosemary to garnish.