Slice the tomatoes about half a centimetre thick, and set aside.
In a bowl, mix 2 tbsp grated parmesan with the thyme and mustard powder.
Lay the puff pastry on a baking tray lined with parchment paper.
Sprinkle 2 tbsp breadcrumbs over the center, leaving a border of about 4 cm uncovered.
Sprinkle the cheese mixture evenly over it.
Starting from the center, arrange the tomato slices in overlapping concentric circles.
Sprinkle the remaining breadcrumbs and parmesan on top, season with a little pepper if you like, and fold the uncovered edge of the pastry over the tomatoes.
Brush the galette with the beaten egg, and bake for 30–40 minutes, until the pastry is cooked through and golden brown.