Sprinkle the yeast over the warm water in a small bowl, and let it dissolve.
Heat the milk and 1/4 cup of the butter together in a small saucepan until the butter is melted. Pour the milk and butter into a large mixing bowl, and stir in the sugar, salt and vanilla extract. Let the mixture cool to lukewarm, and add the yeast. Beat in the eggs. Gradually mix in the flour, adding only as much as is needed to make a smooth dough. Turn the dough out onto a floured surface, and knead until it is satiny.
Rinse and dry the bowl, and coat it lightly with oil. Place the dough back in the bowl, and turn it over so that it is covered with a film of oil. Cover the bowl with a towel, and set the bowl aside in a warm place until the dough rises to double its original size, about 1 1/2 hours. While the dough is rising, butter a 12 x 9-inch baking pan. Prepare the Topping.
Knead the risen dough lightly, and roll it out into a rectangle about 10 x 12 inches.
Melt the final 1/4 cup of butter, and spread it on the dough. Sprinkle with the cinnamon and brown sugar. Roll up the dough carefully from one of the rectangle's longer sides. Cut the roll into slices about 1 inch thick. Arrange the slices over the topping in the baking pan. Cover the pan loosely, and let the dough rise until it is doubled in size again.
Bake the rolls 30 minutes or until they are golden brown. Run a knife around the inside edge of the pan and invert the rolls onto a plate or tray. Serve the rolls immediately, or let them cool and reheat them, covered, the following morning.
Scatter the brown sugar, pecans, and butter bits in the dish, and drizzle with the corn syrup. Place the pan in the oven, and set the oven to 350° F.
Heat the pan for a few minutes, until the butter has melted and the syrup is runny. Remove the pan from the oven, but leave the oven on. Stir the mixture if it has melted unevenly. Set the pan aside.Servings: about 1 1/2 dozen