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 bowl. 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 to coat. Cover loosely with plastic wrap. Let stand at room temperature until doubled, about 1½ hours.