In a large mixing bowl, beat together sugar, tea and butter until pale and fluffy. Add in the oil, followed by the eggs, milk, and vanilla extract; mix well.

Whisk together the flour, baking powder, and salt. Slowly incorporate this into the wet ingredients, one cup at a time. The dough will be soft and slightly sticky. Roll into a ball, wrap in plastic wrap, and refrigerate at least 1 hour or up to 2 days.

Preheat oven to 350 °F and line two baking sheets with parchment paper.

Divide chilled dough into 4 portions. On a generously floured surface, roll out each piece to a 1/6” thickness. The dough will be fairly sticky, so continue to flour as you work with the dough.

Use a 3.5” circle cutter to cut out as many circles as possible from the dough; gather up scraps and continue to roll again.

Move the circles of dough to the prepared baking dishes. Spoon one and a half to two teaspoons of filling into the center of the circle. Shape into triangles by folding up three sides over the filling and push down on the corners.

Refrigerate the cookie sheet with unbaked hamantaschen for at least 20 minutes before baking.

Bake for approximately 20 minutes, or until the cookies are barely golden. Cool on a wire rack. Best consumed within 3 days – the cookies will get a little soggy after that, thanks to the fruit preserves.