Combine 1 t sugar and water in a 1 cup container. Sprinkle the yeast over the top and stir. Let stand until foamy (about 10 min).
Combine remaining sugar, milk, salt, mustard, red pepper, and butter in small saucepan and heat until butter melts. Pour in large bowl and cool to lukewarm.
Add eggs, yeast mixture, and 2 c flour. Beat with wooden spoon until smooth and slightly "stringy" (about 2 min). Stir in shredded cheese. Gradually add remaining flour until dough is stiff and sides of bowl are clean.
Turn dough onto floured surface. Knead until smooth and elastic, 5 to 10 minutes, adding more flour as needed to prevent sticking. Put dough in large greased bowl, turning to coat. Cover with clean towel and let rise in warm place, away from drafts, until doubled in bulk (about an hour).
Punch dough down and turn onto work surface. Knead in diced cheese until evenly distributed. For large loaf, divide dough into three and shape each section into a ball. Place balls in a row in greased 9x5x3 in loaf pan. For smaller loaves, divide into six sections, shape into balls, and put 3 balls in a row in each of two greased 8.5x4.5x2.625" loaf pans. Cover with clean towel and let rise in warm place, away from drafts, until doubled in bulk, about 45 minute.
Brush with Egg Wash for glossy crust (for a dark brown surface: milk, evaporated milk, or egg yolk mixed with water; for shiny finish: whole egg beaten with water; shiny surface that doesn't brown as much as previous: egg white mixed with water).
Preheat oven to 375 and bake 40–45 min for large loaf or 30–35 min for smaller. If crust browns too quickly, tent with aluminum foil. Place on wire racks to cool. For a softer crust, brush bread with oil or melted butter as soon as it comes out of oven.