In a stand mixer fitted with the paddle attachment or in a food processor, combine the plant-based butter, powdered sugar, flour, and vanilla. Mix on low speed until the mixture resembles coarse crumbs.
Add the egg and continue mixing just until a smooth dough forms. Do not overmix. Shape the dough into a flat disc, wrap tightly in plastic wrap, and chill for 1 hour.
Heat the oven to 350°F/175°C. Line two baking sheets with parchment paper.
On a lightly floured surface, roll out the dough to ½ inch/1.25 cm thickness. Using a floured 2-inch/5 cm round or fluted cookie cutter, cut out an even number of cookies. For half the cookies, use a smaller cutter (around ¾ inch/2 cm) to cut out a hole in the center.
Transfer the cookies to the prepared baking sheets, spacing them slightly apart. Chill the trays for 10 minutes before baking to help the cookies hold their shape.
Bake for 12 to 14 minutes, until the edges are pale golden. Let cool on the trays for 5 minutes, then transfer to a wire rack to cool completely.
Dust the top cookies (the ones with holes) generously with powdered sugar. Spoon or pipe about 1 teaspoon of jam onto the flat side of each bottom cookie. Carefully place the tops over the jam to form sandwiches.
Let rest for 30 minutes before serving to allow the jam to settle. Store in an airtight container for up to 3 days.