Preheat the oven to 350°F (180°C). Spray a donut pan with nonstick spray and set aside.
In a bowl, whisk together the melted butter, oil, sugars, and corn syrup.
1/4 cup (56g) salted butter, melted , 3 Tbsp canola oil, ½ cup (123g) brown sugar, ¼ cup (58g) granulated sugar, 1 Tbsp corn syrup
Whisk in the egg and then sour cream until smooth.
1 egg, ¼ cup (60g) sour cream
Add the milk and vanilla, mixing until combined.
⅓ cup (78ml) milk, 2 tsp vanilla extract
Add flour, corn starch, baking powder, salt, and nutmeg to the bowl and whisk, stirring until a thick batter is reached.
1 ¾ cups (266g) all-purpose flour, 2 Tbsp corn starch, 1 ¼ tsp baking powder, ½ tsp salt, ⅛ tsp ground nutmeg
Transfer the batter to a piping bag or a gallon zip-top bag with the corner snipped. Pipe the batter into the prepared donut pan, filling each segment about ½ full.
Bake for 10–12 minutes or until the donuts have risen and feel firm when tapped.
Immediately flip the pan over to remove the donuts from the pan. Allow the donuts to cool completely. Repeat with remaining batter, if needed.
To make the icing of your choice, combine all ingredients except the powdered sugar. Microwave until the butter is melted and the mixture is warm, then whisk until smooth.
Whisk in the powdered sugar until fully combined. Add additional milk, 1 teaspoon at a time, until the icing reaches your desired consistency.
Dip the top of each donut into the icing and top with sprinkles, if desired.
Store in an airtight container for up to 2 days.