Preheat oven to 350 degrees Fahrenheit. Line a muffin pan with paper liners and set aside.

In an electric mixer, beat the eggs and granulated sugar on high speed until fluffy. Add the oil, orange juice, flour, baking soda, cinnamon, salt, walnuts, and carrots, and mix well to form a batter. Fill muffin liners halfway.

Combine the flour and sugar in a small bowl. Cut in the cold butter until crumbly, then mix in the walnuts.

Sprinkle over the batter and bake muffins for 18–20 minutes. Set aside to cool.

In a bowl, use an electric mixer to beat the butter, cream cheese, confectioners’ sugar, and coconut. Transfer to a pastry bag or a plastic zip-top bag fitted with the closed-star tip.

Working with one muffin at a time, insert the tip into the center and fill with frosting, finishing with a star swirl on top.