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Mix together 1/4 cup flour, Parmesan cheese, thyme, dill, and salt in a shallow dish. Pour 1/2 cup milk and 1/2 cup flour in two separate shallow dishes. Dip tilapia fillets into plain flour, then milk. Thoroughly coat the fillets with the seasoned flour; reserve the remaining seasoned flour. Melt butter in a large skillet over medium-high heat. Brown the fillets in the butter, about 2 minutes each side. Reduce heat to medium-low and continue to cook until the fish is easily flaked with a fork, 2 to 5 minutes more. Transfer the fillets to a dish. Increase heat to medium, and pour the remaining seasoned flour into the skillet. Whisk in white wine; cook and stir until reduced and thickened, about 5 minutes. Gradually stir in 1/4 cup milk. Reduce heat to low and allow sauce to simmer for 1 or 2 minutes more. Spoon sauce over tilapia to serve.