Prepare the Oven and Pan: Preheat the oven to 425°F (218°C). Line a 12-count muffin pan with cupcake liners or coat it with nonstick spray, then set aside.
Make the Crumb Topping: In a small bowl, combine the brown sugar, granulated sugar, cinnamon, and melted butter. Add the flour and gently work it in with a fork until loose crumbs form. Do not continue mixing until the mixture becomes a paste. Refrigerate the crumb mixture while preparing the muffin batter so the crumbs remain firm during baking. Combine the Dry Ingredients: In a medium bowl, whisk together the flour, baking soda, baking powder, cinnamon, and salt. Set the mixture aside.
Cream the Butter and Sugars: Using a handheld mixer or stand mixer fitted with a paddle attachment, beat the softened butter, granulated sugar, and brown sugar on high speed for about 3 minutes, scraping down the sides of the bowl as needed, until smooth and creamy.
Add the Orange Zest: Add the orange zest and beat on medium speed for 1 minute, allowing the zest to blend thoroughly into the butter mixture.
Blend the Wet Ingredients: Add the eggs, yogurt or sour cream, and vanilla. Beat for 1 minute, then increase the mixer to high speed and continue until the mixture is combined and mostly creamy. A slightly curdled appearance is fine. Scrape down the bowl as needed.
Finish the Batter: Reduce the mixer to low speed and add the dry ingredients along with the orange juice and milk. Mix only until no pockets of flour remain. Gently fold in the cranberries, taking care not to over-mix. The finished batter will be thick.
Fill the Muffin Cups: Divide the batter among the prepared muffin cups, filling each one all the way to the top. Distribute the chilled crumb topping over the batter and gently press it down so it adheres. If you are skipping the crumb topping, sprinkle the muffins evenly with coarse sparkling sugar instead. Bake the Muffins: Bake at 425°F for 5 minutes. Without opening the oven door, reduce the temperature to 350°F (177°C) and continue baking for 16–19 minutes, or until a toothpick inserted into the center comes out clean. The total oven time is approximately 21–24 minutes, usually closer to 21 minutes when the crumb topping is omitted. Cool the Muffins: Let the muffins rest in the pan for 5 minutes, then transfer them to a wire rack. Allow them to cool for at least 15 minutes before adding the icing.
Prepare the Orange Icing: Whisk the confectioners’ sugar and fresh orange juice together until combined.
Glaze the Muffins: Drizzle the orange icing over the muffins while they are warm or completely cooled.
Store the Muffins: Keep iced or plain muffins covered at room temperature for a few days, or refrigerate them for up to 1 week.