Assemble all the ingredients and check that you have everything.
Before you begin preparing your dough, cut your tomatoes into 1/4 inch slices.
Place the tomato slices into a suspended colander and salt them lightly before allowing them to stand.
Combine your flour and half a teaspoon of salt in a large bowl or food processor.
Disperse the cubed butter (1/2-inch chilled cubes) into your flour.
If using a food processor, pulse eight to ten times, otherwise, mix by hand until a crumbly texture is reached.
Dispense your flour mixture into a large bowl and sprinkle the ice water over.
Use either a rubber spatula or your hands (lightly oiled) to press the dough into a sticky consistency. Add more water spoon by spoon as needed.
Once your dough is sticky but pliable, transfer to a floured surface.
Roll the dough into a disk that's roughly 4-inches in diameter
Enclose the Galette dough in plastic wrap and let it cool in the fridge for an hour.
Preheat your oven to 375°F and align the middle rack while preparing a lined baking tray with parchment paper.
Transfer the chilled dough to a clean, floured surface and allow it to stand for 10 minutes.
Roll the dough into a disk with a diameter of roughly 12-inches or a little bigger than the average dinner plate, and then place it on your prepared baking tray.
Begin preparing your tomato topping by shaking off all excess juices in the colander.
Mix the tomatoes, garlic, thyme, thinly sliced shallot, pepper, and half a teaspoon of salt together with just enough oil to coat them.
Coat the Galette dough with a light layer of dijon mustard while leaving a 1 1/2 inch thick border around the edges.
Dust the Galette base with semolina to ensure moisture doesn't seep through.
Sprinkle your choice of cheese over the mustard-coated base generously.
Cover the coated interior with your tomato mixture.
Place either a single or double-layer of overlapping pepperoni slices, leaving the border unfilled.
Sprinkle Parmesan everywhere except the border as the next layer.
Fold the edges of the dough to roughly 1 inch over the filling. At every 2 inch measure, overlap the dough and pinch it to secure the folded border.
Brush the entire Galette with a beaten egg or milk, making sure to cover the folded edges well.
Transfer to your oven and bake for 45 to 50 minutes or until the crust turns golden and the tomato begins to bubble.
Remove the Galette and allow it to cool on a wire rack for 10 minutes.
Scatter roughly chopped basil over the top and slice into segments and serve
Enjoy this savory pie!