Arrange tomato slices in a single layer on doubled paper towels. Sprinkle lightly with kosher salt. Gently press another paper towel on top. Allow to sit for 10 minutes to release juice.
Preheat the oven to 425°F. Brush a 9 x 9 inch tart pan or similar with melted butter. Fit pie crust into buttered tart pan. Prick the bottom with a fork, brush with remaining butter. Bake for 8 minutes. Set aside to cool slightly. Lower oven temperature to 350°F.
In a small mixing bowl whip together cream cheese, mayonnaise, fresh chives and garlic with a hand mixer until fully combined.
Spread evenly over bottom of crust. Sprinkle with 1/2 shredded sharp cheddar cheese.
Arrange tomato slices over cheese overlapping. Season with black pepper. Sprinkle with remaining shredded cheese and Parmesan.
Bake at 350°F for 35 minutes until the edges are golden and the cheese is bubbly.