Step 1: Sprinkle the gelatin over 1/2 cup of water and let stand until softened, about 5 minutes.
Step 2: Meanwhile, place the egg whites and cream of tartar in the bowl of a stand mixer. Beat until soft peaks form, starting on the slow speed for about 2 minutes, then beating on medium for about 4 minutes, and finally on high for about 2 minutes; the total beating time will be about 8 minutes. If the whites begin to stiffen before the sugar syrup is ready, lower the beater speed to medium-low.
Step 3: While the egg whites are beating, make a sugar syrup: Combine the sugar and corn syrup in a heavy saucepan over high heat and stir just to mix. Cover the pan and cook for 2 minutes. Remove the lid, attach a candy thermometer to the side of the saucepan, and let the sugar cook until it registers 240 degrees F on the candy thermometer.
Step 4: Once the sugar mixture has reached 240 degrees, remove it from the heat and quickly whisk in the softened gelatin, making sure that it fully dissolves. Pour the sugar mixture in a slow steady stream into the egg whites as they beat at high speed. Drizzle in the vanilla and orange liqueur, if using, and continue beating the marshmallow mixture until it is room temperature, 15 to 20 minutes. Spoon the mixture into the oiled baking dish, smoothing the top with a spatula. Let the marshmallow rest in a cool dry place at room temperature until firm, 4 hours or overnight.
Step 5: Cut out the marshmallows: Run the tip of a paring knife around the inside of the baking dish to loosen the marshmallow. Generously dust a work surface with confectioners’ sugar. Turn the marshmallow out onto the dusted work surface, shaking the baking dish if necessary to release it. Using a long, slender knife, cut the marshmallow the short way into six 2-inch strips. Then make 7 cuts the long way at 1-inch intervals to create 48 rectangular marshmallows. Generously dust each of these with confectioners’ sugar to keep them from sticking together. Place the marshmallows on a serving plate or in a bowl. The recipe can be prepared to this stage a day or two — even several weeks — ahead. If made ahead, store the marshmallows in an airtight cookie tin, placing sheets of plastic wrap between each layer. They can be refrigerated in the tin for several weeks.