Cut the Butter at Room temperature in small cubes and place them on a deep plate. With a fork, mash them quickly to remove any hard bits.
Place the Flour, Semolina Flour, Cornstarch and Salt in a large bowl.Add the Butter and work with your adds to create small crumbs. To do so, take a little bit of butter and flour and rub it in between your palms and fingers. After a few minutes, your dough should look like small crumbs.
Add a little bit of water and knead the dough into a ball. Start with only a little bit of water and add more if the dough is too hard. If it turns the dough to something really sticky, add a little bit more flour.
Cover with Cling Wrap and place in the fridge for at least 30 Minutes.
In the meantime, place all the ingredients for the Pesto in a blender and mix in small pulse to form the sauce. Set aside.
To Assemble the Mini Galettes
Preheat your oven on 160'C and line a baking tray with baking paper.
Knead the Shortbread crust for a minute to re-heat it and cut in four.Pour some flour on your kitchen bench and roll each dough into a small circle. Try to roll it as thin as possible without breaking.Place the 4 galette crusts on your lined baking tray.
Brush some Pesto on the Galette crust.Cut the Cherry Tomatoes in half and place them over the Pesto, leaving the edges free to fold over. Fold the edges of the Shortcrust dough over the Cherry Tomatoes to create a Galette.Optional: brush some beaten Egg Yolk over the Galette edges to create a nice coloration in the oven.
Bake for 20 to 25 minutes.
When ready to serve, sprinkle some hand-torn Fresh Mozzarella and Chopped Basil Leaves.