Preheat oven to 375 degrees F. Line a 12-cup standard muffin tin with paper liners and set aside.If making the blueberry swirl, do this first. Combine blueberries, sugar and flour in a food processor and blitz until smooth. Let stand for 10 minutes to thicken.
In a large bowl, whisk together the flour, baking powder, salt, nutmeg, and ½ cup sugar.In another large bowl, whisk together eggs and remaining ¼ cup sugar until frothy. Whisk in vanilla and milk. Whisk in the melted butter and oil. Using a rubber spatula, fold the egg mixture into the flour mixture until just combined. Toss the frozen blueberries and chopped peaches in a teaspoons of flour and immediately fold them through the batter. Divide mixture evenly between paper liners, filling each about ¾ full. Combine 2 tablespoons sugar and ¼ teaspoon cinnamon in a small bowl. Sprinkle tops with the cinnamon-sugar mixture. If making swirled muffins, spoon a teaspoon of the blueberry mixture over each muffin and swirl it through with a wooden skewer.
Bake for 5 minutes, then reduce temperature to 350 degrees F and bake until the muffins are puffed and lightly golden, about 15 minutes longer. A skewer inserted in the center should come out clean. Transfer the pan to a wire rack and let stand 5 to 10 minutes. Turn out the muffins onto the rack to cool further. Serve warm.