Step 1

In a saucepan, bring 2 cups broth and 2 cups water to a boil; season with salt and pepper. Whisk in grits. Reduce heat to medium-low and simmer, partially covered and whisking occasionally, until tender, 30 to 50 minutes (depending on grain size and desired texture). If grits become too stiff before turning tender and creamy, whisk in more hot water a little at a time.

Step 2

Meanwhile, melt 1 tablespoon butter in a large skillet over medium-high heat. Add sausage and cook, breaking into bite-size pieces, until just cooked through and crisp in places, 5 to 6 minutes. Transfer to a paper-towel-lined plate with a slotted spoon, leaving fat in skillet.

Step 3

Add 1 more tablespoon butter to skillet along with onion, bell pepper, celery, and thyme; season. Reduce heat to medium-low and cook, stirring occasionally, until vegetables are tender but not developing any color, 4 to 5 minutes. Season shrimp, add to skillet, and cook, stirring a few times, until opaque and just cooked through, 4 to 5 minutes.

Step 4

Transfer mixture to a bowl; cover to keep warm. Add remaining 3/4 cup broth to skillet and bring to a simmer, whisking to remove any browned bits from bottom. Remove from heat.

Step 5

Remove grits from heat; stir in cheese and remaining 2 tablespoons butter until melted and smooth. Toss tomatoes and celery leaves with oil; season. Serve grits with shrimp mixture, sausage, pan sauce, and tomato salad.