Step 1

In a large bowl, combine the shortening, sugar (or honey) and salt. Pour the boiling water over and stir until the shortening is melted. Set aside to cool until lukewarm.

Step 2

Meanwhile, in a small bowl, sprinkle the yeast over the warm water and whisk until dissolved. Let stand 5 minutes. Using a wooden spoon, stir the yeast into the shortening mixture until thoroughly mixed.

Step 3

Stir in the egg, mixing well. Add the flour 1 cup (125 grams) at a time, stirring after each addition until well blended. Cover tightly and refrigerate overnight.

Step 4

The next day, remove the dough from the refrigerator and set aside in a warm place. Cover loosely with a damp, clean kitchen towel. Let the dough rise until doubled in size, 2 to 4 hours.

Step 5

Butter two muffin tins. Divide the dough in half and on a lightly floured surface, roll the dough into two (12-inch) logs. Divide each log into 12 equal pieces. (This is easiest to do by dividing each log in half, dividing each half in half again, and eye-balling three equal pieces per quarter.) Roll each piece into a ball, then place in the muffin tins. Brush the tops with the melted butter and sprinkle with flaky sea salt. Cover loosely with clean kitchen towels and let rise in a warm place until the dough balls reach the top of the pan, about 1 hour.

Step 6

While the dough is rising, preheat the oven to 375 degrees with the racks in the middle and lower third of the oven.

Step 7

Bake the rolls 25 to 30 minutes, swapping the tins from top to bottom and rotating them front to back, until lightly browned. Brush with melted butter immediately. Let cool about 10 minutes and serve warm or at room temperature.