While the dough chills in the fridge, place a layer of paper towels onto your work surface. Arrange the tomato slices in a single layer then evenly sprinkle the kosher salt on top. Allow the tomatoes to sit for 10 minutes to draw out any excess moisture. After 10 minutes, gently pat the tops of the tomatoes with paper towels to absorb any moisture.
Preheat the oven to 400℉. Line a large baking sheet with parchment paper.
Once the crust has chilled, lightly dust your work surface and the top of the dough with flour. Roll the dough out into a circle about ¼ inch thick and 14 inches in diameter. Roll the crust onto your rolling pin to transfer the dough onto the lined baking sheet. Unroll the crust from the rolling pin so that it's centered and laying flat on the baking sheet.
Spread the garlic and fine herbs cheese in an even layer onto the crust, leaving 2-3 inches around the border. Layer the tomato slices on top within the border of the cheese spread. Season the tomatoes with salt and pepper. Fold the edges of the dough partially onto the filling. Continue going around all the edges and folding the crust up onto the filling.
In a small bowl, whisk together the egg and milk until combined. Use a pastry brush to coat the edges of the dough with the egg wash. Sprinkle the grated parmesan cheese on top of the crust.
If the crust has become too soft and warm, place it in the fridge for 20 minutes before baking. Bake the galette in the oven for 30-45 minutes until the crust is golden brown. Remove the galette from the oven. Tear the fresh basil into pieces and sprinkle them on top. Allow the galette to cool until slightly warm before slicing and serving. Enjoy!