For the sauce: Stir the mayo, yogurt, pickles, dill mustard, lemon zest, lemon juice and some salt and pepper together in a small bowl until well incorporated.
For the shrimp and grits: Preheat the oven to 400 degrees F. Add the polenta rounds to a bowl and toss gently with some olive oil and salt. Place the polenta rounds on a cooling rack set over a sheet tray in one layer and bake for 20 minutes.
Meanwhile, heat a large skillet over medium heat and add the butter and remaining 1 1/2 teaspoons olive oil. Once the butter melts, add the garlic and cook for about 2 minutes, being careful not to burn the garlic. Stir in the shrimp, smoked paprika and some salt and pepper. Cook until the shrimp is pink on both sides and cooked through, about 5 minutes. Turn off the heat and stir in the parsley and chives. Remove the polenta and allow to cool slightly.
To assemble, add one shrimp to each polenta round and top with a generous dollop of sauce, garnish with a dill sprig.