Heat milk in a small saucepan over medium heat until it begins to bubble, about 5 minutes. Sir in salt, shortening, and 1/2 cup sugar. Let cool until lukewarm, at least 10 minutes.
Dissolve yeast in a bowl of 1/4 cup warm water. Pour into the milk mixture; add flour and eggs. Mix well; cover loosely with damp cloth and let dough rise until doubled in volume, about 1 hour.
Punch down dough. Cover and let rise again until doubled in volume, about 40 minutes.
Place dough on a lightly floured surface. Roll into three 9x15-inch rectangles. Spread each rectangle with 2 tablespoons butter.
Mix 3/4 cup brown sugar and cinnamon together in a bowl. Sprinkle mixture equally over the 3 rectangles. Roll each rectangle tightly beginning at the long side. Cut into 9 equal slices, yielding 27 rolls total.
Preheat oven to 375 degrees F (190 degrees C).
Combine 1 1/2 cups brown sugar, 3/4 cup butter, pecans, and corn syrup in a bowl. Sprinkle mixture equally into 3 baking pans.
Bake in the preheated oven until caramel is bubbly, 5 to 10 minutes. Remove from oven and place 9 rolls in each pan. Let rise again until doubled in volume, about 40 minutes.
Bake in the hot oven until golden brown, about 30 minutes. Invert rolls onto another dish or aluminum foil immediately. Serve warm.