Preheat oven to 375 degrees. Line a 10-cup standard muffin tin with paper liners; set aside. Combine 2 tablespoons sugar and 1/4 teaspoon cinnamon in a small bowl; set aside. In a large bowl, whisk together the flour, baking powder, salt, nutmeg, and remaining 3/4 cup sugar and 1/2 teaspoon cinnamon; set aside.
In another large bowl, whisk together eggs, vanilla, and milk. Whisk in the melted butter. Using a rubber spatula, fold the egg mixture into the flour mixture until just combined. Dividing evenly, fill each of the 10 muffin cups halfway with batter.
Distribute the plum pieces evenly among the cups (about 3 tablespoons per muffin), scattering them over the batter. Spoon the remaining batter on top, dividing evenly. Sprinkle tops with the reserved cinnamon-sugar mixture.
Bake, rotating the pan halfway through, until the muffins are puffed and golden brown and a cake tester inserted in the center of one muffin comes out clean, 15 to 17 minutes. Transfer the pan to a wire rack and let stand 5 to 10 minutes. Turn out the muffins onto the rack to cool a few minutes. Serve warm.