In the bowl of your stand mixer, place the vegan butter and the icing sugar, and mix well on medium-high speed for 3-5 minutes until light and fluffy. If you don't have a stand mixer, you can use a hand-held mixer for this.
Add vanilla and beat to incorporate.
Add the salt and the thyme.
Add the flour in 2-3 portions, beating on low speed. Mix only until the flour is just incorporated.
Scrape the dough out of the bowl and onto a large sheet of plastic wrap. Form into a disc, wrap tightly, and store in the fridge for at least a couple of hours, or overnight.
Preheat oven to 350 degrees.
Divide you dough in half and flour your work surface and the top of the dough. With a rolling pin, roll the dough out until it's between 1/8" and 1/4" thick.
Using a large star-shaped cookie cutter, cut as many cookies as you can. Remove to the side, then smush all the remaining dough back together, re-roll, and cut again, and repeat until you are out of dough.
Line the stars on a cookie sheet, and then with a small star cookie cutter, cut small stars out of the centre of every second cookie. You can add these small stars to the scrap dough to be re-rolled and re-cut as well.
Bake in preheated 350 degree oven for about 9-10 minutes. Edges may be golden, but you don't want your cookies to brown. The tops should be dull.
Remove from the cookie sheet to wire rack to cool.
Once cool, lay your large, uncut stars out, upside-down, on a board. Microwave the jam for about 30 seconds, and then stir it well. This will help it to be easier to work with. Drop a dollop of jam on each star, then top with a cut cookie star to make a sandwich.
Dust with icing sugar.
Store in a airtight container at room temperature for up to 3-5 days, or in the freezer for up to 3 months.