How to Make It
Preheat oven to 400°F. Bring stock and 1 teaspoon of the salt to a boil in a medium saucepan over high. Whisk in grits; cook, whisking often, until smooth, about 20 minutes. Whisk together cooked grits, cheese, tomato paste, and egg in a bowl. Set aside until ready to use.
While grits cook, heat oil in a large skillet over medium-high. Add onion, mushrooms, and carrots. Cook, stirring occasionally, until vegetables are softened, 7 to 8 minutes. Add garlic, thyme, and 1/4 cup of the scallions; cook, stirring occasionally, 2 minutes. Stir in tomatoes and wine. Bring to a boil over high; reduce heat to medium-low, and simmer, stirring occasionally, until slightly thickened, 4 to 5 minutes. Stir in shrimp, pepper, and remaining 2 teaspoons salt. Remove from heat.
Spread grits mixture into a 13- x 9-inch casserole dish. Top evenly with shrimp mixture. Cover with aluminum foil. Bake in preheated oven until casserole is bubbly and shrimp are cooked through, about 18 minutes. Remove from oven; let stand 5 minutes. Sprinkle with remaining 1/4 cup scallions.