Preheat the oven to 350°F. Grease a 12-count muffin tin with additional butter (as noted in the ingredients).

In a large bowl, whisk together 1 1/2 cups all-purpose flour, 1/2 cup sugar, 1 1/2 teaspoons baking powder, 1/2 teaspoon salt, and 1/4 teaspoon nutmeg.

Melt 5 tablespoons unsalted butter and let it cool slightly. In a separate small bowl, lightly beat the egg with a fork. Add the warmed 1/2 cup milk and the melted 5 Tbsp butter to the beaten egg and stir to combine.

Pour the wet mixture into the dry ingredients and stir gently until just combined. The batter should be lumpy—do not overmix.

Divide the batter among the prepared muffin cups, filling each about one-third full.

Bake for 20–22 minutes, or until the muffin edges are golden and a toothpick inserted into the center comes out clean. Remove the muffins from the oven.

While the muffins are baking or immediately after removing them, prepare the topping: in a small bowl mix 1/3 cup sugar with 3/4 teaspoon cinnamon. In another small bowl melt 3 tablespoons unsalted butter.

When the muffins are warm (not piping hot), dip the top of each muffin briefly into the melted 3 Tbsp butter, then immediately dip or roll the buttered top (and sides, if you like) in the cinnamon‑sugar mixture to coat.

Place the coated muffins on a wire rack to cool slightly before serving.