Preheat oven to 200C/400F.
Depending on how big you want your galette to be, use 1-2 sheets of puff pastry to create a circle of your desired size. Do this in on a piece of parchment paper. No need to be perfect, you can Frankenstein it.
Leaving an inch border, spread your pesto onto the frozen puff pastry evenly. Then decoratively arrange the slices of tomatoes on top of the pesto. Season the tomatoes with salt and pepper.
Fold the border over the tomatoes. Brush with egg and bake for 25-30 minutes or until the puff pastry is golden brown.
Top with stracciatella and basil.