Preheat oven to 375 degrees. Thoroughly grease one 24-cup mini muffin pan or two 12-cup mini muffin pans.
In the bowl of a stand mixer fitted with the paddle attachment, beat together eggs, sugar, vanilla and grand marina on medium speed for approximately 3 minutes. Stir in melted butter until combined.
Sift together flour, cornstarch, baking powder and salt. Gradually add to the wet ingredients until combined. Stir in orange zest.
Fill each mini muffin cup approximately three-quarters full with the batter. Bake for 10 minutes, or until the edges are golden brown. Remove from oven and cool for 5 minutes. Remove muffins from the tin to finish cooling on a cooling rack. Dust with powdered sugar. Store in an airtight container for up to 2 days, but they are best served the same day.