Warm the milk in a microwave-safe measuring cup for 15–20 seconds until it feels warm to the touch. Sprinkle the yeast over the milk and let it proof for 5–10 minutes, until foamy.
In a food processor, pulse together the sugar, flour, and salt. Add the chilled butter, cubed, and pulse until the mixture resembles coarse crumbs.
Stir the eggs and orange zest into the yeast mixture. With the food processor running, slowly pour in the liquid until the dough forms a ball. Add up to 1/4 cup more milk if the dough seems too dry.
Transfer the dough to a lightly floured surface and knead for 2–3 minutes until it becomes smooth and elastic.
Place the dough in a lightly oiled bowl, cover with a towl, and let it rise in a warm spot for 2 hours, or until doubled in size.
Roll the dough into a 10x16-inch rectangle on a floured surface.
Spread the cranberry sauce evenly across the surface, leaving a small border around the edges.
Starting at the long edge, roll the dough tightly into a cylinder. Pinch the seam to seal.
Slice the log into 11–12 rolls, about 1–1.5 inches thick.
Arrange the rolls in a greased baking dish, leaving a little space between each for rising.
Cover with a towel and let rise for another hour.
Preheat your oven to 375°F (190°C).
Brush the tops of the rolls generously with the orange syrup.
Bake for 25–30 minutes, or until golden brown.
While still warm, brush the buns with more syrup for a glossy, flavorful finish