Heat milk in a small saucepan over medium heat until it begins to bubble, about 5 minutes. Stir 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.