Lightly flour two pieces of parchment paper and have two more pieces nearby.
In a large bowl, whisk together the flour, starch, baking powder, and sea salt. Set aside.
In a large mixing bowl using a hand mixer or stand mixer fitted with the paddle attachment, beat together the vegan butter and sugar on high for 2 minutes. Add the milk and vanilla and beat for another 30 seconds. Use a spatula to scrape down the sides of the bowl.
Turn the mixer on low and slowly add the dry ingredients to the wet. Increase the speed to medium and beat until just incorporated.
Divide the dough into two equal pieces. Place each on one of the floured pieces of parchment paper and then cover each mound of dough with one of the extra sheets of parchment paper. Use a rolling pin to roll each mound of dough into a ⅓-inch-thick oval or rectangle. Fold in the edges of the parchment to secure each dough disc and then wrap with foil or plastic wrap. Refrigerate for at least 1 to 2 hours to chill and firm the dough.
Once the dough is chilled and you're ready to bake, preheat the oven to 350Line three large baking sheets with parchment paper. Lightly flour a clean work surface.
Unwrap each piece of dough and use your cookie cutters of choice (I used heart-shaped and star-shapeto punch out the dough. Transfer the the cookies to the lined baking sheets, being sure to leave about 2 inches of space between each. (If you're using varying sizes of cookie cutters, divide the cookies between sheets based on similar sizes. For instance, I used four sizes of heart-shaped cookie cutters, so I placed the two smaller sized cookies on one sheet and two larger sized cookies on the other. That way, if baking time varies, you can simply pull one tray out earlier than the other rather than having to individually remove cookies.)
Re-roll the dough and repeat until as much of the dough is used up as possible.
Bake for 10 to 16 minutes (could be less or more than this time range depending on the size of your cookies, so keep a close watch), or until the bottom, pan-touching edges of each cookie are just beginning to turn light golden brown.
Let the cookies cool on the baking sheets for 5 minutes, then carefully transfer to wire cooling racks to cool completely.
Meanwhile, prepare the vegan royal icing.
Once the cookies have cooled completely, ice them and decorate to your heart's content.
Store the finished cookies at room temperature for up to 3 days or refrigerate for up to one week.