Dissolve yeast in warm water in the bowl of a stand mixer fitted with the dough hook. Stir in sugar and salt until you see foam rising. Add 3 cups flour and 3/4 cup shortening; mix with the dough hook until the mixture is the consistency of a thick pancake batter.

Fill a pot with hot (not boiling) water.

Remove the mixer bowl and cover it with plastic wrap and a towel. Place the bowl over the pot of hot water, making sure the bottom does not touch the water. Let rise until doubled in size, 45 minutes to 1 hour.

Place the bowl back on your stand mixer and gradually mix in remaining 4 cups flour until dough is smooth and elastic; you may need to add up to 1 additional cup.

Heavily grease two 9x13-inch glass pans with shortening.

Divide dough into 24 balls. Place 12 balls into each of the prepared pans; cover with plastic wrap and a towel. Let rise in a warm area until doubled in size, about 1 hour; balls will start out at about 1 1/2 inches in diameter but will rise and touch the sides of the pans.

Preheat the oven to 375 degrees F (190 degrees C).

Bake rolls in the preheated oven until golden brown on top, 25 to 30 minutes. Remove from the oven and brush melted butter over top.