To make the dough, melt the ½ cup butter in a small saucepan over medium-low heat. Add the milk and granulated sugar and heat just to lukewarm (about 100°F), stirring to dissolve the sugar.

Pour the warm milk mixture into a bowl. Stir in the yeast. Allow the mixture to sit for 10 minutes. Stir in the salt. Beat the whole egg and yolk together and add to the yeast mixture. Stir in the flour I cup at a time until you have a sticky dough.

Scrape the dough out onto a floured work surface and knead, about 5 minutes, adding a little more flour as necessary, until you have a nice smooth dough. Butter a large bowl. Place the dough in the prepared bowl and cover with plastic wrap. Put the bowl in a warm place and allow the dough to rise for 2 hours until tripled in volume.

Meanwhile, prepare the pan. Spray a 9 × 13-inch baking pan with vegetable oil spray or brush it with butter.

To prepare the sugar-pecan topping, melt the butter with the brown sugar and corn syrup in a small saucepan over medium-low heat, stirring to combine. Remove from the heat and spread the mixture over the bottom of the pan. Sprinkle with the chopped pecans.

Punch down the dough and turn it out of the bowl onto a lightly floured work surface. Knead for a minute, then use a lightly floured rolling pin to roll the dough into a rectangle about 15 × 12 inches and 1/8 inch thick.

To make the cinnamon sugar filling, melt the butter in a small saucepan over medium-low heat and allow it to cool. Brush the butter thoroughly over the surface of the dough. In a bowl, mix together the granulated sugar and cinnamon. Sprinkle the cinnamon sugar evenly over the melted butter. Roll the rectangle up, like a jelly roll, along one long edge.

Slice the log of rolled dough into 1-inch-thick slices and arrange the slices, cut side up, in the prepared pan. Cover the pan with a piece of plastic wrap (you can spray the wrap with vegetable oil spray to be sure it doesn’t stick to the dough) and allow it to rise in a warm place for about 40 minutes.

Preheat the oven to 350°F. Bake the schnecken until golden brown, 35 to 40 minutes. Check them occasionally during the baking time and, if they seem to be browning too quickly, cover them with a sheet of aluminum foil.

Remove the pan from the oven. Allow the schnecken to cool for 5 to 10 minutes, then turn them out of the pan while still warm by inverting the pan over a large platter or a baking sheet. Serve warm.