In one pan, melt 1/4 cup butter over medium heat. Saute the onion, carrot, celery, pepper, and tomato in the melted butter until soft. Using a blender or food processor, puree vegetables with vegetable broth; set aside.
In a separate pot, melt the remaining 1/2 cup butter. Slowly whisk in flour, and then stir in half and half. When warm, slowly stir in cheese until melted. Mix in veggie puree, and serve.