Preheat oven to 170°Celsius.
Measure dried cranberries into a small saucepan. Soak with orange juice for 10 minutes. Simmer for 3 to 5 minutes while stirring continuously.
Remove from heat and add the candied orange peel. Set aside to cool.
In a measuring jug, mix the oil, buttermilk, and egg lightly with a hand whisk lightly with a hand whisk. Set aside.
In a large bowl, sift the flour, baking powder, baking soda, and salt. Add sugar and mix with a whisk until the ingredients are well blended.
Make a well in the center and pour in the wet ingredients. Mix to form a thick batter.
Add the dried cranberries and orange peel to the batter. Mix well.
Fold in the grated orange rind.
Pour the batter into prepared muffin casings and bake for 20 minutes.
Remove muffins from the oven and let them cool completely before frosting.
To make the orange glaze, mix the powdered sugar with orange juice until smooth. Transfer into a piping bag and pipe the orange glaze in a circular motion on each muffin.