Preheat the oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners or grease the cups.
In a large bowl, whisk together the all-purpose flour, granulated sugar, baking powder, baking soda, and salt until well combined.
In a separate medium bowl, whisk the Greek yogurt, vegetable oil, eggs, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and gently fold together until just combined. Do not overmix; the batter should be slightly lumpy.
Fold in 1/2 cup Nutella gently into the batter to create a marbled effect, leaving some streaks of Nutella visible.
Divide the batter evenly among the 12 muffin cups, filling each about 3/4 full.
Using a small spoon or toothpick, swirl a small additional amount of Nutella on top of each muffin to create a decorative swirl.
Bake in the preheated oven for 18 to 20 minutes or until a toothpick inserted into the center of a muffin comes out clean or with a few moist crumbs.
Remove the muffins from the oven and allow them to cool in the tin for 5 minutes, then transfer to a wire rack to cool completely before serving.