Combine sugar, salt, grated cheese, and scalded milk; stir until cheese is melted. If necessary, return to heat and heat just until cheese is melted. Cool cheese mixture to lukewarm.
Dissolve yeast in lukewarm water; stir in lukewarm cheese and milk mixture. Add about half of the flour and beat until smooth. Stir in enough remaining flour to make a stiff dough. Turn onto a lightly floured surface and knead until smooth and elastic, adding a little more flour as necessary to keep dough from sticking. Put in a large buttered bowl; turn to butter both sides or brush more butter on top of dough. Cover with a clean dish cloth and let rise in a warm place (about 80 to 85° )until doubled in bulk, about 1 hour.
Turn dough out onto lightly floured surface; divide in two equal portions. Knead each portion lightly and shape into two loaves. Place in greased 9x5x3-inch loaf pans; cover with cloth and let rise again for about 1 hour, until doubled in bulk. Bake at 350° for 35 minutes.
When done, loaf will sound hollow when lightly tapped.