Combine granulated sugar, brown sugar, orange juice, water, cinnamon stick, and salt in a saucepan over medium-high heat. Bring to a boil while stirring until the sugar dissolves, about 2 minutes, with a steady rolling bubble across the surface.

Add fresh cranberries to the boiling syrup and return to a boil. Once boiling, reduce heat and simmer at a gentle boil for 10-12 minutes, stirring often, until most berries burst and the sauce thickens to a spoon-coating consistency.

Remove the saucepan from the heat and stir in orange zest and vanilla extract. Discard the cinnamon stick, then cool to room temperature for 30-60 minutes until no longer hot.

Chill the cranberry sauce until it thickens further, at least 2 hours, covering the surface to prevent a skin from forming. The sauce should become glossy and sliceable when served.