Prepare your vegan egg according to package instructions, and set aside.
In a large bowl, use a hand mixer to beat the vegan butter and sugar together until creamy. Add the egg replacer, non-dairy milk, vanilla extract, and lemon juice, and mix well.
In a separate bowl, whisk the flour, baking powder, and salt.
Add the dry ingredients to the wet ingredients and beat until a soft dough forms.
Gently pat the dough into a ball, wrap with plastic wrap or place in an airtight container, and chill for at least 1 hour (or up to 24 hours).
Cover two cookie sheets with parchment paper or a silicone mat.
Remove the dough from the fridge and transfer to a lightly floured surface. Divide the dough into two parts. Roll out the first part to about ¼" thick, sprinkling with more flour if needed to keep the dough from sticking to the rolling pin.
Press a round cookie cutter (about 2" in diameter) into the dough and place the cutout onto the cookie sheet. Repeat until you have used all of the dough (you can re-roll the remaining scraps until all of the dough is used).
Repeat with the second piece of dough.
Place about ½ - ¾ teaspoon of filling, such as fruit jam, vegan hazelnut-chocolate spread, or poppy seed filling, into the center of each round.
For each round, fold the left side of the circle over towards the filling, then do the same with the right side to form a point at the top. Fold up the bottom edge and tuck the bottom right corner under the right side, then pinch each corner of the hamantaschen to seal it.
Place the cookie sheet into the freezer for at least 10 minutes. Meanwhile, preheat the oven to 400°F.
Bake the hamantaschen for about 10 minutes, until the edges are golden. Allow them to rest on the cookie sheet for 10 minutes, before transferring to a wire rack to cool completely.