Preheat the oven to 180C (355F) and line a muffin tin with 12 muffin liners.
Into a mixing bowl, sift the flour, salt, and baking powder. Whisk to combine and set aside.
In the bowl of a stand mixer fitted with a paddle attachment (you can use a bowl and a hand mixer instead), add the butter and sugar. Beat for 2 minutes or until fluffy.
Then, add the oil, orange zest, and vanilla extract. Beat until homogenous in consistency. Scrape the bottom and the sides of the bowl and beat again.
Add one egg at a time and beat until well combined.
Mix the milk and orange juice in a small bowl.
Add the dry ingredients in three parts to the eggs and butter mixture – alternating with the milk mixture, starting and ending with the dry ingredients – while beating on low until a homogenous and silky consistency is reached. The pattern should look like this: dry/milk/dry/milk/dry. Scrape the bottom and the sides of the bowl and mix on low again.
Toss the cranberries with some flour and then fold them into the muffin's batter using a rubber spatula.
Spread the batter between the muffin liners so they’re ⅔ full. Bake for 25-27 minutes or until a toothpick inserted in the center comes out clean.
Remove from the oven and let cool down for 5-10 minutes in the pan. Then, place it onto a cooling rack to cool down completely.
When the muffins are at room temperature, whisk the glaze ingredients in a bowl and drizzle on top of the muffins.