Make the dough. In a medium-large mixing bowl, whisk together 2 ¾ cups all-purpose flour, sugar, instant yeast, and salt. Set aside.

In a small saucepan over medium-low heat, melt butter and milk together until just warm to the touch, about 95-110 degrees.

Crack the egg into a small mixing bowl. Whisking constantly, add the butter/milk mixture in a thin stream until completely combined. Add mixture to the dry ingredients and fold together. A shaggy dough should form and be pulling away from the bowl. Gradually add flour in 2 tablespoon increments until it pulls away a bit.

Turn dough onto a floured surface and knead 5-6 minutes, until smooth. Gather dough into a ball and place it in an oiled bowl, making sure to get a little oil on all sides. Stretch some plastic wrap over the top and allow dough to rise in a warm, draft-free environment for 40 minutes or until doubled in bulk.

In the meantime, line two rimmed baking sheets with parchment. Set aside.

Make the filling. Combine sugar and orange zest in a small bowl. Rub together with your fingers to release the oils in the zest. Use a fork to stir in cardamom and salt.

Shape the buns. Return dough to floured surface. Flour a rolling pin and roll dough into an 18×12-inch rectangle. Brush dough with butter, leaving a ½-inch border on all sides.

Mentally divide the dough into thirds, like an unfolded letter. Place half the sugar mixture in the middle third of the dough—it’ll be a 12×6-inch section surrounded by two buttered sections of the same size.

Carefully grab one short side of the dough and fold it over the center, so that the dimensions are now 12×12-inches. Brush the top of the folded section with more butter and scatter on the remaining sugar mixture. Fold the other short side over the top so that the dimensions are 12×6-inches. Tap edges 'closed' with your rolling pin.

Carefully lift and turn dough over so that the seam is against the floured surface. Roll the dough so that the dimensions are 14×8-inches.

Use a large, sharp chef’s knife to trim the short edges of the dough by about ½-inch. Slice dough into 12 strips. Working with one strip at a time, twist the ends until you have a loosely-twisted rope of dough. Carefully bring ends toward one another until they cross over one another and create a small hole. Tuck ends into that hole. Place shaped buns on prepared pans, leaving about 6 inches of space between.

Cover pans loosely with wax paper (or parchment) and let rise in a warm, draft-free environment for another 25-30 minutes. Remove wax paper (or parchment).

Place oven racks in the center positions. Preheat oven to 375F. Bake buns for 10 minutes. Rotate pans top-to-bottom and front-to-back. Bake another 7-8 minutes, or until golden brown.

While buns are baking, make the glaze. Combine orange juice and sugar in a small saucepan over medium-low heat, stirring frequently until sugar dissolves (about 3-5 minutes). Remove from heat and stir in cardamom and butter.

Use a pastry brush to brush warm buns with glaze. Buns are best the day they are made, but will keep in an airtight container at room temperature for a day or so.