1 envelope (1 tablespoon) active dry yeast
1 cup whole milk
1/4 cup vegetable shortening
3 tablespoons sugar
1 1/2 teaspoons salt
1 large egg, room temperature
3 1/2 cups all-purpose flour, plus more for surface
Vegetable oil (for bowl)
1/4 cup unsalted butter
Flaky sea salt (like Maldon or Diamond Crystal kosher)
13x9-inch baking dish
Whisk yeast and ¼ cup warm water (110°-115°) in a small bowl; let stand 5 minutes.
Heat milk in a small saucepan over medium until just warm. Combine shortening, sugar, and kosher salt in a large bowl. Add warm milk; whisk to blend, breaking up shortening into small clumps (it may not melt completely). Whisk in yeast mixture and egg. Add 3½ cups flour; stir vigorously with a wooden spoon until dough forms. Knead dough with lightly floured hands on a lightly floured surface until smooth, 4–5 minutes. Transfer to a lightly oiled bowl; turn dough to coat lightly with oil. Cover loosely with plastic wrap. Let stand at room temperature until doubled, about 1½ hours.
Preheat oven to 350°. Melt butter in a small saucepan. Lightly brush 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 12”x6" rectangle.
Cut lengthwise into three 2"-wide strips; cut each crosswise into three 4”x2" rectangles. Brush half of each (about 2”x2") with melted butter; fold unbuttered side over, allowing a ¼-inch overhang. Place flat in 1 corner of dish, folded edge against 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 at least 30 minutes or up to 6 hours.
Bake rolls until golden and puffed, 25–35 minutes. Brush with butter; sprinkle with sea salt. Serve warm.
Makes 36 rolls.