How to Make It
Bring 3 cups water, milk, and 2 teaspoons salt to a boil in a large heavy saucepan over high. Whisk in grits, and cook, whisking constantly, 45 seconds, scraping bottom and sides as needed. Return to a boil; cover and reduce heat to medium-low. Cook grits until tender, 20 to 25 minutes. (For a looser texture, whisk in 2 to 4 tablespoons water halfway through cooking.)
Meanwhile, melt 2 tablespoons butter in a large skillet over medium-high. Add half of the shrimp, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Sauté until shrimp are almost pink, 5 to 6 minutes. Toss with 1/2 tablespoon lemon juice, and transfer to a plate. Repeat with 2 tablespoons butter and remaining shrimp, salt, pepper, and lemon juice.
Add chives and remaining 2 tablespoons butter to grits. Top with shrimp, tomatoes, and Salsa Verde.