In a mixing bowl, or in a stand mixer fitted with a paddle attachment, whisk together the flour, sugar, baking powder, and salt. Add the vegan butter and vegan cream cheese, cutting them into the dry ingredients until the mixture resembles coarse crumbs.
Pour in the orange juice, orange zest, and vanilla extract. Mix until a dough forms. Knead briefly on a lightly floured surface until smooth. Transfer the dough to an airtight container and refrigerate for at least 2 hours or up to overnight.
For the poppy seed filling, grind the poppy seeds in a spice grinder or blender until finely ground. In a saucepan, combine the plant-based milk, sugar, lemon juice, lemon zest, vanilla extract, and salt. Bring to a simmer over medium heat, stirring until the sugar dissolves. Add the ground poppy seeds and continue to cook, stirring frequently, until thickened, 3-5 minutes. Remove from heat and let cool completely before using.
For the prune filling, blend the prunes, lemon juice, lemon zest, Cointreau (if using), maple syrup, cardamom, and salt in a food processor for 2 minutes. Let the contents of the food processor sit for 10 minutes,and then process again for 60 seconds until mostly-smooth. If the mixture is too thick, add a small amount of warm water, 1 teaspoon at a time, until spreadable. Set aside.
Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
On a lightly floured surface, roll out the chilled dough to ⅛-inch (3 mm) thickness. Using a round cookie cutter or the rim of a glass, cut out 3-inch (7.5 cm) circles. Place 2 teaspoons of the desired filling in the center of each circle.
To shape the hamantaschen, lift three edges of the dough and pinch them together to form a triangle, leaving a small opening in the center. Transfer to the prepared baking sheet, spacing them slightly apart.
Bake for 12-15 minutes, until the edges are lightly golden. Let cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.