Parker House Rolls

Whisk one ¼-oz. envelope active dry yeast (about 2¼ tsp.) and ¼ cup warm water (110°–115°) in a small bowl; let sit until foamy, about 5 minutes.

Heat 1 cup whole milk in a small saucepan over medium until just warm. Combine ¼ cup vegetable shortening, 3 Tbsp. sugar, and 1½ tsp. Diamond Crystal or 1 tsp. Morton kosher salt in a large bowl. Pour in warm milk, whisking constantly to blend and break up shortening into small clumps (it may not melt completely). Add yeast mixture and 1 large egg, room temperature and whisk to combine. Add 3½ cups (438 g) all-purpose flour and stir vigorously with a wooden spoon until a dough forms. Turn dough out onto a lightly floured surface and knead with lightly floured hands until smooth, about 5 minutes. Lightly coat a large bowl with vegetable oil; transfer dough to bowl and turn to coat. Cover loosely with plastic wrap. Let sit in a warm spot until doubled in size, about 1½ hours.

Lightly brush a 13x9" baking dish with some of the ¼ cup unsalted butter, melted. Punch down dough; divide into 4 equal pieces. Working one at a time, roll out pieces on a lightly floured surface to a 12x6" rectangle. Cut lengthwise into three 2"-wide strips; cut each strip crosswise to make three 4x2" rectangles (9 total per piece). Brush half of each rectangle (about 2x2") with melted butter, then fold unbuttered side over buttered side, leaving ¼" uncovered at the end. Place rolls, flat side down, starting in a corner of prepared dish, so folded edge is against a short side of the dish. Add rolls side by side to form a long row, then repeat with remaining rolls until you have 4 rows. Brush tops with melted butter, loosely cover with plastic, and chill at least 30 minutes and up to 6 hours.

Preheat oven to 350°. Bake rolls until golden and puffed, 25–35 minutes. Brush with more butter and sprinkle with flaky sea salt. Let cool slightly before serving.