Lightly butter a large bowl. In a small pot on medium heat, heat milk until it is warm to the touch. Pour warm milk into the bowl of a standing mixer fitted with the dough hook. With mixer on low, add yeast, granulated sugar, salt, melted butter, cinnamon, nutmeg, cardamom, and prepared egg-replacer.
Put the mixer on lowest speed and begin adding flour, 1 cup at a time, until a soft, slightly sticky dough forms. If mixture is too dry or firm, add a little more non-dairy milk. Continue kneading for about 4 to 5 minutes, scraping down hook and sides of bowl as necessary. Turn dough out onto floured surface and knead by hand for another couple of minutes. Alternatively, you can mix this in a large bowl and knead by hand.
Shape dough into a smooth ball, and place in the buttered bowl. Using your hands, lightly coat the top of the dough with a little butter from the bowl. Cover bowl tightly with plastic wrap and let dough rise in a warm place until doubled, about 1 hour 15 minutes. You can also store the dough overnight in the refrigerator, then let it come to room temperature before using.
Line a baking tray with parchment paper. Turn dough out onto a lightly floured work surface, and knead briefly. Divide dough into 24 equal pieces, about 2 ounces each, about the size of an extra large golf ball. With your hands, shape pieces into smooth, tight balls, and place on baking tray, about a 1/2 inch apart. Cover with plastic wrap, and let rise in a warm place until touching and doubled in size, 45 minutes to 1 hour.
Preheat oven to 375°F. In a small bowl, stir together the syrup and water. Brush tops of buns with the syrup wash. Using very sharp scissors or a very sharp paring knife rubbed with oil, slice a cross into the top of each bun. Transfer tray to oven, and bake until golden brown, about 20 to 25 minutes. Transfer pan to a wire rack to cool.
To make the glaze: In a medium bowl, whisk together powdered sugar, lemon juice, and non-dairy milk. Scrape icing into a plastic baggie and snip the corner. Make a snip smaller than you think you want it. Pipe the glaze over buns where the cross was cut and set aside so the glaze can set, or eat immediately.
