Preheat oven to 425F (215C) and line a 12-count muffin tin with paper liners. Set aside.
In a large mixing bowl, whisk together flour, sugar, cornstarch, baking powder, baking soda, and salt until combined.
In a separate bowl or measuring cup, whisk together melted butter and vegetable oil. Whisk in egg and vanilla extract until combined, then stir in sour cream.
Add sour cream mixture to dry ingredients and use a spatula to gently fold together until about 50% combined.
Add white chocolate chips, then continue to gently stir batter until completely combined (don’t over-mix or muffins will be dense and dry).
Fill prepared muffin liners about halfway full with muffin batter. Use a clean small spoon to make a divot or small nest in the center of each liner.
Take your ¾ cup of Nutella and dollop a Tablespoon of Nutella into the nest that you created in each muffin tin. Use your spoon to gently nestle it into the divot.
Top muffins evenly with remaining batter and use spoon to gently work muffin batter evenly around Nutella filling. The muffin cups will be fairly full but you will use all or nearly all the batter.
Briefly warm remaining (¼ cup) Nutella in the microwave until it is easily stirrable with a spoon. Drizzle Nutella over the muffin tops and use a butter knife to gently swirl over the surface. Top with coarse sugar, if using.
Transfer muffin tin to center rack of preheated oven and bake for 8-9 minutes, then, without opening the oven door, reduce heat to 350F and bake an additional 10-12 minutes, until muffin tops are beginning to turn light golden brown and muffins are baked through.
Allow to cool in muffin tin for 5-10 mins before carefully lifting and transferring to a cooling rack to cool completely before enjoying.