This dough is a basic sweet dough. I use it for cinnamon rolls and monkey bread, as well. Combine the milk, yeast, and sugar in a mixing bowl. Let stand for 2 minutes to proof the yeast. Add the egg, butter, nutmeg, salt, and half of the flour. Mix until smooth, then beat for 2 minutes. Stir in enough of the remaining flour to make a soft dough.
Turn dough onto floured surface and knead just enough to smooth the dough and thoroughly combine ingredients. Kneading makes gluten, so don't overdo it, or you'll lose tenderness. Place in a greased bowl, cover and let rise until doubled, about 1 1/2 hours.
To assemble, punch the dough down, and divide in half. Roll the dough into discs and spread into the greased pans. Cover and let rise in the pan until doubled, about 1 1/2 hours. Meanwhile, mix the sugars and cinnamon in a bowl. Canned peach slices are usually too thick. Slice them as necessary to get reasonably thin pieces, about 1/2 inch.
When the cakes are risen, brush the dough with melted butter, and sprinkle with a mixture of sugars and cinnamon. Spread peaches over the top, covering as much dough as possible, and then sprinkle again with the sugar and cinnamon mix. You want a good, thick coating of sugar, to glaze the top.
Bake in a 350-degree Fahrenheit oven for 20-25 minutes. The coffee cakes should be golden around the edges, but somewhat pasty where risen between the peach slices. Let cool for at least 15 minutes.