Heat the neutral cooking oil in a wide pot over medium heat. Add the remaining half of the aromatics and cook, stirring frequently, for 4-5 minutes until softened.
Add the halved cherry tomatoes and season every with salt and pepper. Cook in an even layer for 5 minutes until the cherry tomatoes soften and begin to char. Add the butter to the pot and stir frequently, whisking it into the released tomato juices. Taste and season again with salt and pepper.
Pour the stock into the pot and scrape up any browned bits stuck to the bottom. Taste and season and bring to a boil. Reduce heat to medium-low.