To make the sauce: In a small bowl, whisk together mayonnaise, buttermilk, horseradish, Parmesan, sour cream and ranch dressing mix. Cover and refrigerate until ready to serve. Can be made up to 1 week in advance.
To make the tomatoes: In a large skillet or Dutch oven, heat 1/2-inch oil over medium-high heat until it reaches 350 degrees. Line a plate or wire rack with paper towels.
While oil is heating, in a pie plate, whisk egg, then whisk in milk, 1/2 teaspoon salt and pepper.
In another pie plate, combine flour, cracker crumbs and remaining 1/2 teaspoon salt. Dip tomato slices into egg mixture, turning to coat. Dredge both sides of tomato slices in flour mixture and shake off excess flour. Carefully place tomato slices into hot oil. Do not crowd the pan. Fry until golden brown, turning once, about 4 minutes per side. Drain on paper towels and serve immediately with sauce. Garnish with basil, if desired.