In a small bowl, combine the paprika, cayenne, garlic powder, dried thyme, dried oregano, 1/4 teaspoon kosher salt, and black pepper; mix until evenly blended.
Spritz both sides of the shrimp lightly with olive oil spray and rub to coat, then evenly coat the shrimp with the spice mixture.
In a medium saucepan, bring 2 cups of the chicken broth, the milk, water, and 1 teaspoon kosher salt to a gentle boil, watching carefully to avoid boiling over.
Slowly stir in the grits, then reduce heat to the lowest setting, cover, and simmer for 28–30 minutes, stirring after 5 minutes and occasionally thereafter to prevent sticking; add more water if the grits become too thick.
When the grits are smooth and creamy, remove from heat and stir in the butter, 1 ounce of the grated cheddar, and the Parmesan; keep warm.
Just before the grits finish, heat a large cast-iron or heavy skillet over medium-high heat and warm briefly with a little oil (or use olive oil spray).
Add the coated shrimp to the hot skillet and cook until the spices darken and the shrimp turn opaque, about 2 minutes per side.
Transfer the grits to 4 plates, sprinkle the remaining grated cheddar over each, then arrange the shrimp on top.
Add the remaining 1/2 cup chicken broth to the skillet to deglaze, cook for about 1 minute over medium heat until reduced by half, and drizzle the pan juices over the plated shrimp and grits.
Garnish with sliced scallions and serve immediately with lime wedges.
