Dissolve yeast and sugar in 1 cup lukewarm water. Let stand for 10 minutes, then stir well; it should be foamy on top. If it’s not, buy new yeast and try again. Bring 1 cup water to a boil and pour it into a large bowl. Add oats, butter, sorghum and salt. Let the mixture stand 5 minutes to cool and then stir to blend evenly. Add egg and beat well.

Add whole-wheat flour and 2 cups unbleached flour, and stir with a wooden spoon until a soft dough forms. Sprinkle ½ cup flour on a clean counter and turn the dough out of the bowl onto surface. Knead with floured hands, adding enough of the remaining flour to keep dough from being too sticky to handle.

Knead until the dough is smooth, soft and a tiny bit sticky, about 10 minutes. Form dough into a ball and transfer to an oiled large bowl, turning to coat. Cover bowl with plastic wrap and allow it to rise at warm room temperature until doubled in bulk, 1½ to 2 hours. (You can also refrigerate it overnight.)

Lightly butter two 8½- by 4½-inch loaf pans. Turn out dough onto a lightly floured surface and knead several times to remove air. Divide dough in half and shape each half into a loaf, then place in pan. Drape a kitchen towel over the pans and set aside until the loaves have risen nearly to the top of the pans, about an hour.

Heat oven to 350°, with oven rack in the middle position. Mix a teaspoon or so of sorghum with a little water and brush the tops of the loaves with the mixture (this will help the loaves brown). Bake 50 to 60 minutes. Bread should be brown and sound hollow when tapped on the bottom.

Transfer to a rack to cool completely, about 1½ hours.

Slice with a serrated knife.