Bring the broth to a gentle boil in a medium pot over medium heat.
Stir in the stone-ground grits, then reduce heat to low and cook, stirring frequently, until thick and creamy, about 20-25 minutes.
Meanwhile, season the shrimp with salt, pepper, paprika, and cayenne pepper, letting them sit while you prepare the sauce.
Heat the oil in a large skillet over medium-high heat until shimmering, then add the shrimp in a single layer.
Cook the shrimp for 2-3 minutes per side until they turn pink, slightly caramelized, and smell sweet and smoky. Remove and set aside.
Add butter, minced garlic, and chopped scallions to the same skillet, cooking for 1-2 minutes until fragrant and slightly softened.
Pour in ½ cup of chicken broth and squeeze in lemon juice, scraping up any browned bits from the bottom of the pan.
Let the sauce simmer for 2 minutes until slightly reduced and fragrant.
Return the shrimp to the skillet, tossing to coat in the sauce, and cook for another minute until heated through and flavorful.
Stir in grated cheddar cheese into the cooked grits until smooth and melted, adjusting seasoning as needed.
Taste the grits and add more salt, pepper, or lemon juice as desired for brightness and balance.
Serve the creamy cheese grits on plates, topped with the smoky, spicy shrimp and sauce, garnished with chopped scallions.
