Preheat the oven to 350 degrees F. Butter an 8-inch cast iron skillet.
Add the 2 tablespoons of butter to a medium-sized saucepan over medium heat. Once the butter foams, add the shallots and garlic and saute until tender, about 3 to 4 minutes. Stir in the tomato paste, then add the chicken broth, and whipping cream and bring to a simmer.
Once simmering, slowly and gradually whisk in the grits. Keep stirring until the grits become thick, about 8 to 10 minutes. Add the chopped sun-dried tomatoes and stir until thoroughly mixed. Season with salt and pepper, to taste.
Add the grits to the prepared skillet and top with the crumbled goat cheese. Bake for about 25 to 30 minutes. Remove the skillet from the oven and let cool for 5 to 10 minutes before serving. Slice into triangles and serve.