Make The Pastry:

Food Processor Method:

• Add the flour, butter, salt, and Parmesan cheese to the bowl of a food processor. Pulse until the mixture resembles breadcrumbs, about 5 to 10 seconds. With the processor running, pour the cold water slowly through the feed tube just until the dough comes together. (You may not need all of the water).

By-Hand Method:

• Add the flour, butter, and salt to a large bowl. Using your fingertips or a pastry cutter, rub the butter into the flour until it resembles coarse breadcrumbs. Stir in the Parmesan cheese. Drizzle in the cold water and mix with a fork until the dough starts to hold together, then gently bring it into a ball with your hands.

Chill and Roll:

• Wrap the dough in plastic wrap and refrigerate for 1 hour or overnight.
• Dust a clean work surface with flour and preheat your oven to 400°F (200°C).
• Remove the pastry from the fridge; since it will be firm, let it warm slightly so you can roll it. Roll the dough into a 14-inch (36 cm) circle. Roll over the rolling pin and transfer to a 10-inch  a low-sided cast-iron skillet. Allowing the excess to hang over.

Assemble And Bake:

• Cover the pastry evenly with the grated Gruyère cheese, leaving a 1-inch border all around that hangs over the edge of the skillet. Arrange the tomato slices on top of the cheese, keeping them within that inner circle. Combine the rosemary and black pepper in a small bowl and sprinkle evenly over the tomatoes.
• Fold the bare edges of the pastry inward over the outer edge of the tomatoes, pleating as you go. Brush the exposed pastry crust with the egg wash.
• Bake for 20 to 25 minutes until the crust is golden and crisp. (Note: If the galette puffs up in the center, this is just from steam and will go down as it cools).

Cool And Serve:

• Remove from the oven and allow the galette to cool in the pan for 10 minutes. Sprinkle the top with the chopped basil before slicing and serving.