These yeasty pillows of perfection are easy to make and especially terrific when you have a large group of people to feed. All you need is a little time and patience and you'll have your guests cooing with delight at your homemade rolls.
In a small bowl, add the water and yeast and whisk together. Let sit for 5 minutes while the yeast bubbles up and activates.
Heat 1 cup whole milk in a small saucepan over medium heat just until warm. Combine 1/4 cup vegetable shortening, 3 tablespoons sugar and 1 1/2 teaspoons kosher salt in a large bowl. Add the warmed milk and whisk to blend, breaking up shortening into small clumps (it may not melt completely and that is fine). Whisk in the yeast and water mixture and add the room-temperature egg. Mix well to combine and break up the egg.
Now add 3 1/2 cups all-purpose flour and stir vigorously with a wooden spoon until a dough forms. With lightly floured hands, knead the dough on a lightly floured surface until smooth, about 4-5 minutes. Transfer the dough to a lightly oiled bowl and turn to coat. Cover loosely with plastic wrap and let stand at room temperature until doubled in size, about 1 1/2 hours.
Preheat oven to 350°. Melt 1/4 cup unsalted butter in a small sauce-pan. Lightly brush a 13x9-inch baking dish with some melted butter. Punch down dough; divide into 4 equal pieces. Working with 1 piece at a time, roll out on a lightly floured surface into a 12x6-inch rectangle.
Cut lengthwise into three 2-inch-wide strips; cut each crosswise into three 4x2-inch rectangles.
Brush half of each (about 2x2-inch) with melted butter and fold unbuttered side over, allowing 1/4-inch overhang. Place flat in 1 corner of dish, folded edge against the short side of dish. Add remaining rolls, shingling to form 1 long row. Repeat with remaining dough for 4 rows.
Brush with melted butter, loosely cover with plastic, and chill for 30 minutes or up to 6 hours. Bake rolls until golden and puffed, 25-35 minutes. When the rolls are cooked to a golden perfection, brush with butter, sprinkle the tops with Maldon flaky sea salt and serve warm.