Dissolve the yeast in the warm water and let it stand until foamy.
Stir in the warm milk, granulated sugar, half of the melted butter, and egg.
Add flour and salt gradually to form a soft dough, then knead until smooth.
Cover and let the dough rise in a warm place until doubled, about 1 hour.
Roll the dough into a rectangle and brush with some of the remaining melted butter.
Combine brown sugar and cinnamon, sprinkle over the dough, and roll it up tightly.
Pour maple syrup into a greased baking pan and scatter the pecans over it.
Slice the dough roll into 12 pieces and arrange them cut-side up in the pan.
Cover and let rise again until puffy, about 30 minutes.
Bake at 350°F for about 25 minutes, until golden and cooked through.
Cool briefly, then invert the pan onto a serving platter while the syrup is warm.