When I was visiting Paris in 2011, I saw macarons, chocolate candies, and even cakes made with green tea powder (matcha). Green tea is an antioxidant and believed to reduce the risks of cancer and heart disease, so this is a hamantaschen that is also good for you. I fill these with apricot jam, but you can substitute any flavor you like. You can find kosher-certified green tea powder (matcha) online.
In a large bowl, mix together the eggs, sugar, oil, and lemon juice and mix well. Add the green tea powder and mix well. Add the flour and salt and mix until the dough comes together. Cover the dough with plastic wrap and leave it in the fridge for one hour to firm up.
Preheat oven to 350 degrees F. Line two or three large cookie sheets with parchment paper or silicone baking mats, or plan to bake in batches. Divide the dough in half.
Take another two pieces of parchment paper and sprinkle flour on one, place one dough half on top, and then sprinkle a little more flour on top of the dough. Place the second piece of parchment on top of the dough and roll on top of the parchment until the dough is about ¼ -inch thick. Every few rolls, peel back the top parchment and sprinkle a little more flour on The dough.
Use a 2- to 3-inch drinking glass or round cookie cutter to cut the dough into circles. Use a metal flat-blade spatula to lift up the circle of dough and place it on another part of the flour-sprinkled parchment paper. Place up to 1 teaspoon of jam in the center of the dough circle and then fold the three sides in toward the middle to form a triangle, leaving a small opening in the center. Pinch the three sides together very tightly. Place on the prepared cookie sheets. Repeat with the remaining dough and roll and cut any dough scraps, making sure to sprinkle a little flour under and over the dough before you roll.
Bake for 14 to 16 minutes, or until the bottoms are lightly browned but the tops are still light. Slide the parchment onto wire racks to cool the cookies. Store in an airtight container at room temperature for up to five days or freeze for up to three months.