Heat olive oil in a saucepan over medium-high heat. Add mirepoix and a small pinch of salt and stir–sauté until soft.
Stir in cherry tomatoes and tomato paste, cooking until a thin layer of fond forms on the bottom of the pan.
Stir in chicken stock and reduce the heat to low. Add tomato sauce, chicken bouillon, and a couple of pinches of kosher salt. Simmer for 18 to 20 minutes. Remove the soup base from heat and allow it to cool for 10 to 15 minutes.
Transfer the soup base to a blender and blend or blend using an immersion blender until smooth and no chunks remain. Season with additional salt to taste, if needed.