Whisk yeast and water in small bowl; let stand for 5 minutes. Heat milk in small saucepan over medium til just warm. Combine shortening, sugar, and salt in 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 flour; stir vigorously with wooden spoon til dough forms. Knead dough with lightly floured hands on lightly floured surface until smooth, 4-5 minutes.
Transfer to lightly oiled bowl; turn to coat. Cover loosely with plastic wrap. Let stand at room temp til doubled, about 1 1/2 hours.
Preheat oven ot 350. Melt butter in small saucepan. Lightly brush a 13x9 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 12x6 rectangle.
Cut lengthwise into three 2" wide strips; cut each crosswise into three 4x2" rectangles. Brush half of each with melted butter; fold unbuttered side over, allowing 1/4" overhang. Place flat in 1 corner of the 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 butter; loosely cover with plastic wrap and chill for 30 min or up to 6 hours.
Bake rolls until golden and puffed, 25-35 minutes. Brush with butter; sprinkle with sea salt.