Make the filling: Combine the jam, mint leaves, and cardamom pods in a saucepan, cover and bring just to boiling over low heat. Remove from the heat. Set a fine-mesh sieve over a mixing bowl and strain the filling through it, pressing and mashing with a wooden spoon to get as much of the filling through the sieve as possible. Discard the remaining pods, leaves and mango pulp, if any. (This will keep in a covered container in the refrigerator for up to a week.)
Make the dough: In the bowl of a stand mixer fitted with a paddle attachment (or, if you are using a handheld mixer, in a large mixing bowl), combine the butter and sugar and mix for about 3 minutes, until creamy, fluffy, and lighter in color. Add the eggs, one at a time, and mix after each addition until incorporated. Add the coconut cream and vanilla and mix until just combined.
Pour the flour, baking powder, baking soda, and salt into a mixing bowl and stir to combine. Add the flour mixture to the butter mixture and mix to form a dough.
Form the dough into 2 flat round discs and wrap each in plastic wrap. Refrigerate for 2 to 4 hours, until fully chilled. (This can be refrigerated for up to 2 days before rolling and baking.)
When you are ready to bake, preheat the oven to 375°F. Line 2 rimmed baking sheets with parchment paper or Silpats and set aside. Lightly flour a work surface and a rolling pin.
Place 1 disc of dough on the work surface and roll out until it is between ¼- and ⅛-inch thick. With a 3-inch cutter, cut out as many rounds as possible (you can collect all the scraps reroll them, but just once). Spoon 1 teaspoon filling into the center of each round and top each with ¼ teaspoon of toasted coconut and a pinch of salt. Fold up the edges to form triangles, pinching them to form points, and leaving a small amount of filling exposed at the top. Repeat with the second disc of dough. You will have 48 hamantaschen.
Lightly flour a large spatula and use it to transfer the hamantaschen to the prepared baking sheet, arranging them about 1½ inches apart, 12 per sheet. (You will need to work in batches.) In a small bowl, lightly beat the egg with the water, and, with a pastry brush, brush it on the dough (but not the filling).
Bake for 13 to 15 minutes, or until the dough is a pale golden color. Cool on the baking sheets for 5 minutes and transfer to racks to cool completely. Repeat with the remaining hamantaschen.
• Mango jam is widely available in supermarkets these days and you can also find it online; Goya makes a tasty, easy to find version.
• Coconut cream is made from the flesh of coconuts. It is very fatty and rich, with a texture similar to thick whipped cream. It’s typically used in tropical cuisines, but kosher cooks and others who rely on dairy-free cooking use it as an alternative to regular cream. Coconut cream is used in recipes from curries to baked goods. It can be purchased at most major supermarkets, Asian specialty stores, or online. Coconut cream should not be confused with cream of coconut, the canned, sweetened product that is used in cocktails and also in baked goods.
• To bruise cardamom place the pods on a cutting board. Using the flat side of a large chef’s knife, (being careful not to have the blade face you), press on the pods very gently so that they just crack without releasing their seeds.
• If you would like to make these pareve, you can substitute an equal amount of nonhydrogenated margarine for the butter.
• Toasted shredded coconut is available in stores, but it’s easy to do yourself. Preheat the oven to 375°F. Scatter the coconut evenly on a rimmed baking sheet and bake, mixing every 3 minutes and watching carefully to make sure that it does not burn, for a total of about 9 minutes, or until lightly browned. Note that sweetened coconut will toast a little faster than unsweetened, so adjust the timing accordingly.