Peel sweet potato and cut into ½-inch cubes. Steam in a saucepan fitted with a steamer attachment until completely tender, about 10 minutes. Transfer sweet potato to a food processor and puree until smooth, or mash to desired consistency with a fork in a bowl. Set aside.
Melt butter in a small saucepan over medium-low heat. Cook, swirling the pan occasionally until the butter is completely melted and the milk solids are starting to brown, about 5 minutes.
Combine warm water, honey and yeast in the mixing bowl of a stand mixer and whisk to combine. Let sit until the yeast becomes foamy, 1 to 5 minutes. Add sweet potato, butter and egg yolk and beat with the dough hook just to mix slightly. Add whole-wheat flour, all-purpose flour, cinnamon, salt, nutmeg and cardamom and mix with the dough hook on low speed until the mixture comes together as a dough, 1 to 2 minutes. Increase speed to medium and let knead until the dough is smooth and elastic, 6 to 8 minutes. Remove dough hook from dough, cover bowl with plastic wrap and let dough rest until it has almost doubled in volume, 1 to 2 hours.
Coat a 9 by 13-inch baking dish with cooking spray. Scrape dough out of bowl with a bowl scraper onto a lightly floured surface and divide into 12 pieces. see snake method here. Tuck edges of dough portions under to create little balls and then round into neat tight balls on counter-top by pressing down the edges of the dough as you circle the dough around. Set dough ball in the prepared dish and repeat with the remaining dough balls, spacing evenly in the dish. Coat a sheet of plastic wrap with cooking spray and gently lay over the surface of the rolls, and let rise 30 minutes.
Preheat oven to 375 degrees F. Beat egg white with a fork in a small dish until foamy. Remove plastic wrap and brush egg white over the tops of the buns. Bake until the buns are golden brown, 43 to 47 minutes.
Let buns cool at least 30 minutes. Mix the confectioners sugar, milk and vanilla in a small bowl until smooth. Decorate buns with a cross pattern with the icing.