Add all purpose flour, whole wheat flour, salt, butter and thyme to a food processor. Pulse till the mixture resembles bread crumbs. Keep pulsing while adding the water till the mixture just about comes together. Transfer this to a work surface, and knead together for 20 seconds till the mixture forms into craggly dough. Flatten into a disk, wrap in clingfilm and chill in the refrigerator for 30-45 minutes.
To make the filling
Mix the pesto that we made earlier (http://myfoodstory.in/basil-walnut-pesto/) and cream cheese to make a smooth paste.
Heat the oven to 190 degree Celsius.
Assembling the Galette
Once the dough is chilled, remove from the refrigerator and place on a heavily floured work surface. Roll the dough out into a 9-inch round. Transfer to a baking sheet lined with parchment paper. Spread the pesto mixture over the dough leaving a 1 inch border. Place the tomato slices on the pesto mixture and sprinkle with salt and freshly ground pepper. Fold the edges over the tomatoes using the 1 inch border and pleat them to make it fit. The center of the pie will be open.
Brush the edges with egg wash (Whisk together egg and a little water to make egg wash) and bake for 40-50 minutes till golden brown. Remove from the oven. Let stand for 5-10 minutes, sprinkle with fresh basil, cut into wedges and serve.