Measure out 3 cups of the broth in a 3-quart saucepan and add the milk and salt; bring it to a boil over medium-high heat stirring often. When it comes to a boil whisk in the grits. Whisk with one hand while slowly pouring the grits in with the other.
Reduce the heat to medium-low and cook, stirring often, 5 minutes or until thickened. Remove from heat and stir in 2 tablespoons of the butter, and cheese, stirring until cheese melts.
While broth mixture is coming to a boil, melt remaining 2 tablespoons of butter with the olive oil a large cast iron or nonstick skillet. Add the onion, bell pepper, and garlic; cook, stirring constantly over medium-high heat, 2 minutes or until onion is tender. Add the shrimp and cook 1 minute or just until shrimp turns pink and the end curls toward the tail. Remove the shrimp with tongs and set aside to prevent overcooking.
Measure out 2 tablespoons of the remaining 1 cup of chicken broth and set aside in a very small bowl for the slurry. Add the remaining chicken broth, tomato paste, Worcestershire sauce and hot sauce to the skillet; bring to a boil over medium heat, stirring occasionally, and cook 3 minutes. Stir in remaining 2 tablespoons of butter until it melts.
Stir together cornstarch and the 2 tablespoons of chicken broth set aside. Stir it into the sauce mixture and stir quickly over medium heat. It should thicken in about 30 seconds. Add the shrimp back to the sauce mixture.
Spoon the cheese grits onto plates. (I served mine in four (5-inch cast iron skillets). If the grits have thickened up too much, stir in a little milk to loosen. Spoon the shrimp mixture over the grits and sprinkle with chopped fresh parsley.