In a large saucepan, bring 4 cups broth, 1½ teaspoons salt, and pepper to a boil over medium-high heat; whisk in grits. Reduce heat, partially cover, and simmer, stirring occasionally, until tender and thickened, about 40 minutes. Remove from heat; stir in 2 tablespoons butter and cream. Stir in 1 teaspoon thyme. Cover until ready to serve.
In a large skillet, heat oil and remaining 1 tablespoon butter over medium-high heat. Add shrimp; sprinkle with remaining ½ teaspoon salt. Cook until shrimp are pink and firm, 1½ to 2 minutes per side. Sprinkle with Creole seasoning. Remove from skillet. Stir remaining ⅔ cup broth into skillet, scraping browned bits from bottom of pan. Stir shrimp into remaining liquid in skillet. Serve shrimp with grits and Roast Beef Debris. Garnish with thyme, if desired.
Recipe by Louisiana Cookin' at https://louisianacookin.com/debris-shrimp-grits/