Spray a 9-inch fluted tart pan with a removable bottom with cooking spray or lightly brush with melted coconut oil.
Pulse the pecans in a food processor until they are coarsely ground. Add the 2 teaspoons coconut oil, maple syrup, flax meal, nutmeg and salt. Process until the mixture comes together. Gather the dough and with your fingers press into and up the sides of the prepared pan.
Preheat the oven to 350°F. Bake about 10 minutes, just until a hint of golden color is around the edges. Cool.
When the tart is cool but not cold, carefully loosen the crust and remove the fluted rim. Transfer to a flat serving platter.
Spread a layer of the apricot fruit spread over the bottom, about 1/8-inch thick, reserving about 2 tablespoon for the top glaze.
Remove the core stem and leaves from the top of the persimmons. Cut them in half. Lay cut side down and cut into thin slices, ¼- to 3/8-inch thick. Arrange the persimmon slices in circles.
Heat 2 tablespoons fruit spread with 1 ½ teaspoons water. Use a pastry brush to apply a thin glaze to the fruit. Finish with a sprinkle of pomegranate seeds.
To easily remove pomegranate seeds: Cut pomegranates in half. Holding one half cut side down in your palm, sharply smack the red skin with a solid wooden spoon. Keep tapping until the brilliant red gems all drop into the bowl.