To make the dough, add water to the bowl of a standing electric mixer. Scatter yeast and a pinch of the sugar over the water’s surface. Stir to combine. Let stand until bubbly, about 5 minutes.

Meanwhile, melt butter in a saucepan over medium heat. Remove from heat and add milk, the remaining 2 tablespoons sugar, and salt. Stir to combine. Add egg and mix well.

Add contents of the saucepan to the yeast mixture along with 2 cups of the flour. Mix by hand or beat with the paddle attachment of a stand mixer until well combined. Add remaining flour, about 1/4 cup at a time, until a smooth but sticky dough forms.

Let the dough rest for 20 minutes. Turn the rested dough out on a lightly floured surface and knead until smooth, adding flour only to keep the dough from sticking. If using a stand mixer, switch to the dough hook and knead for 3 to 5 minutes.

Transfer the dough into a lightly oiled bowl, flipping it to coat the entire surface. Cover with plastic wrap and let rise until doubled in size, about 1 hour.

Grease or parchment-line a baking sheet and melt 4 tablespoons of butter for shaping the rolls.

Turn the risen dough out on an lightly floured surface and divide it in half. Roll out each piece into a 12 by 12-inch square. Brush the top of each square with the melted butter. Give the butter a minute or two to solidify before dividing each square into quarters (a pastry or pizza cutter works great for this). Cut each quarter into three 2-inch wide strips. Roll each strip into a spiral.

Place the spirals on the prepared baking sheet with the open edge of the spiral touching the bottom of the baking sheet. Cover with plastic wrap and let rise again in a warm place for about 30 minutes.

Preheat oven to 375° F. Bake the rolls until golden brown, about 15 to 20 minutes.

Near the end of the baking time, melt remaining 4 tablespoons butter. Brush the rolls with butter immediately after removing them from the oven. Serve warm.