In a large bowl, whisk the dry ingredients. Use a box grater to shred the frozen butter directly into the flour. Toss gently to coat. This "cold-shred" method ensures the butter doesn't melt before it hits the oven, creating flaky layers without the need for yeast.
Pour the cold buttermilk into the center. Stir with a fork just until a shaggy dough forms. Over-mixing at this stage will make the rolls tough.
Turn the dough onto a floured surface. Gently pat it into a rectangle, fold it in thirds like a letter, and pat it out again. Repeat this twice. This "faux-lamination" creates the visual layers seen in yeasted rolls.
Combine the browned butter, brown sugar, cinnamon, and cardamom into a paste. Roll the dough into a ¼-inch thick rectangle and spread the paste to the very edges.
Roll the dough tightly into a log. Use unflavored dental floss or a very sharp serrated knife to slice into 8–10 even rounds. Floss prevents the dough from being squashed during the cut.
Place the rolls in a greased 9-inch round cake pan so they are just touching. This forces them to rise up rather than spread out.
Bake at 400°F for 20–25 minutes until the tops are golden and the center roll springs back when touched.
Whisk the glaze ingredients until smooth and pour over the rolls while they are still warm so it seeps into the spirals.