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In large mixer bowl, combine 2 cups flour and 1 tablespoon dry yeast.
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Heat milk, sugar, shortening, and salt till warm (115-120°), stirring to melt shortening. Add to dry mixture.
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Add eggs. Mix well by hand and then stir in 1 ½ to 2 cups flour, making a moderately stiff dough.
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Knead on a lightly floured surface till smooth (adding more flour as you need it, if needed). Shape into a ball. Place in a greased bowl, turning once. Cover; let rise till double.
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Punch down; divide in half. Cover; let rest 10 minutes.
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Roll each half of sweet roll dough into a 12×8-inch rectangle.
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Brush each with half of the softened butter. Combine granulated sugar and cinnamon; sprinkle over dough.
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Roll up each piece of dough, starting with long side; seal seams. Slice each roll into about 12 pieces.
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In saucepan combine brown sugar, ¼ c butter, and corn syrup. Cook and stir just till butter melts and mixture is blended.
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Distribute mixture evenly in two greased 8-9 inch round baking pans. Top with pecans.
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Place rolls, cut side down, in baking pans (on top of the pecans). Cover; let rise till double.
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Bake at 375 degrees for 18 to 20 minutes. Cool about 30 seconds; invert on rack and remove pans.