Combine water and milk in a large saucepan; bring to a boil. Whisk in grits (or polenta) until smooth. Cover and reduce heat to low. Cook, whisking occasionally, until creamy and thickened, about 25 minutes. Remove from heat.

Stir in Parmesan, 1/2 teaspoon salt and 1/4 teaspoon pepper. Cover and set aside.

Meanwhile, heat 1 tablespoon oil in a large high-sided skillet or large pot over medium heat. Add onion and cook, stirring occasionally, until soft, about 3 minutes. Add garlic and cook for 1 minute. Stir in tomatoes, 2 teaspoons paprika and the remaining 1/4 teaspoon each salt and pepper. Add collards by the handful, letting them wilt slightly after each addition. Continue to cook, stirring frequently, until the collards are tender and beginning to darken, about 10 minutes. Transfer to a bowl and cover to keep warm.

Add the remaining 1 tablespoon oil to the pan and increase heat to medium-high. Toss shrimp with the remaining 1 teaspoon paprika in a medium bowl. Add the shrimp to the pan and cook, stirring occasionally, until they turn pink, 3 to 4 minutes.

Serve the shrimp and collards with the grits.