Defrost the dough sheets according to package directions.
Separate the plum tomatoes from their juice.
Pour the juice, honey and sugar into a frying pan and boil for 3–5 minutes so that the sauce becomes slightly caramelized.
Sprinkle the starch over the apple slices and add them to the pan. Continue to boil for a few more minutes, stirring every now and then. Pour into a flat-bottomed ø 8.7 inch baking dish. Halve the plum tomatoes and put them in the dish. Let cool.
Heat the oven to 392°F.
Using a rolling pin, roll out the puff pastry dough to the size of the baking dish, then place it over the the tomato-apple filling. Push the edges of the pastry a few centimeters below the filling. Brush the pastry with beaten egg and prick its surface with a fork in a few places.
Bake in the oven for approximately 25 minutes, until the pastry has a beautiful color and is done.
After taking it out from the oven, let the tart rest for 15 minutes before upending onto a serving platter.
Mix together the sauce ingredients and serve it with the warm tomate tarte tatin.