In a small sauté pan, melt 1/2 Tbsp butter. Add 1 Tbsp brown sugar, oats, and 1 tsp cinnamon. Reduce heat and stir for about 4 minutes until nutty and aromatic. Remove oat mixture from pan and set aside in a bowl.
In the same pan, add the remaining 1/2 Tbsp butter and 1 Tbsp brown sugar, swirling to combine.
Add the sliced nectarines, vanilla, and nutmeg to the pan. Swirl until the nectarines are coated in the syrup, then turn off the heat.
Spoon Greek yogurt over the oats in the bowl, then top with the warm nectarines.