Preheat the oven to 350ºF. Line a baking sheet with parchment paper and set aside.
Add the flours, starch, salt, gum, and sugar to the bowl of a food processor. Pulse to combine. Cut the butter and shortening into small pieces, add to the food processor and pulse until a sandy texture forms, 10-15 pulses. Pour the water into the food processor, pulsing between each addition, until a dough has formed.
Turn the dough out onto a piece of parchment paper. Knead into a ball, then roll out to 1/8-inch thick. Cut the dough into 3-inch strips, then slice again to form 3x5-inch rectangles. Spoon 1 tablespoon of jam onto one rectangle of dough. Cover with another rectangle of dough, then crimp the edges together with a fork until all sides are closed up. Transfer to baking sheet. Repeat with the remaining dough.
Prick the top of each tart with a fork before baking to allow for air to flow through. Bake on the center rack for 35-45 minutes, until dough has browned. Remove and cool on a wire rack before enjoying.