Oven drying tomatoes is the best way to use up the ones that have lost their lustre: it concentrates the flavour and rids them of excess moisture so you can use them in a variety of dishes over the coming days.
Preheat oven to 250 F.
Working crosswise, slice tomatoes into 3mm slices.
Divide among parchment-lined baking sheets and bake, on the centre rack, for 1 hour.
Remove from oven and let cool while the Phyllo dough defrosts and sesame pesto is made.
Add all Sesame Pesto ingredients to a food processor or blender and blend until all ingredients come together to make a sauce. (If using a blender, adding 1 to 2 tablespoons of water may help with blending).
Preheat oven to 350 F.
Place 1 sheet of Phyllo dough onto a prepared baking sheet (oil) or parchment-lined baking sheet. Lightly brush with olive oil.
Repeat for 5 more layers.
Carefully fold each side inward by 1-inch to form a border crust.
Use a fork to poke holes through phyllo so it doesn’t rise during baking.
Spoon all of the pesto onto the centre of the Phyllo and spread out until it touches the edge of the borders.
Using a spatula, remove tomatoes from the baking sheet and spread evenly over the pesto.
Add to the centre of the oven and bake for 25 minutes. Optional: Broil on high for one minute to attain a more golden crust.
Top with flaked salt, basil leaves and sesame seeds before serving.