Heat oven to 350 degrees with a rack set in the center. Generously oil a 12-cup muffin pan or line with paper liners.
To a large bowl, add the granulated sugar, eggs and oil, and whisk until well combined.
Add the buttermilk, orange juice, salt and orange zest, and whisk until well combined.
Whisk in the baking powder and the baking soda, then use a flexible spatula to fold in the flour and cranberries.
Divide the mixture among the 12 wells and bake until the muffins are puffed and a toothpick inserted in the center comes out with just a few moist crumbs, 18 to 23 minutes. (If using frozen cranberries, the muffins may need to bake for up to about 35 minutes.) Let the muffins cool in the pan for 10 minutes, then turn them out onto a wire rack to cool completely.
While the muffins are cooling, make the glaze, if using: In a medium bowl, whisk together the powdered sugar, 2 tablespoons orange juice, the orange zest and a pinch of salt until smooth. Your glaze should have the same consistency as honey; add a bit more orange juice if necessary.
Glaze the cooled muffins and let the glaze set for 15 minutes before serving. Muffins can be frozen, glazed or unglazed, in an airtight container for up to 1 month.
