In a bowl, combine diced apple, pear, brown sugar, cinnamon, nutmeg, almond extract, and cornstarch. Mix well until incorporated.
Roll out puff pastry, using a bench knife cut the puff pastry at a diagonal (you'll have to large triangles), then cut it again so you'll have 4 triangles. Add ¼ cup filling to one triangle. Carefully fold the triangle over, seal with water, then press the tines of the fork to close the dough. Repeat until all the turnovers are created.
Carefully, move the turnovers to a baking sheet. Brush with remaining apple/pear liquid, and make a slit in each of the turnovers so they can breathe while cooking!
Bake at 350 degrees for 30 minutes or until golden brown. Serve immediately, or let cool to room temperature and store in the refrigerator in a sealed container for up to 3 days.
*You will have extra apple/pear mixture leftover. You can eat it as is or cook it on the stove top on low for 15 minutes to create an apple-pear applesauce! Either way this mixture will not be wasted!