In stand mixer bowl, add 3 cups flour, yeast, sugar, salt and pepper; mix well. In saucepan or microwave-safe dish, heat milk, water and oil to 120-130°F. Add to flour mixture. Add mustard, minced onion and egg. Using a paddle attachment, blend on low speed for 30 seconds; beat on medium speed for 3 minutes.
Switch to dough hook attachment. Gradually stir in enough remaining flour to make a firm dough. Knead until smooth and elastic, about 5 to 8 minutes.(NOTE: For hand mixing: following above steps, mix ingredients in large mixing bowl using a wooden spoon or dough whisk. Knead on floured surface until smooth and elastic.) Place dough in lightly oiled bowl and turn to grease top. Cover; let rise until indentation remains after poking dough with finger down to second knuckle, about 1 hour.
Punch down dough. Divide into 3 parts. Divide each third into 6 pieces. Shape each piece into a smooth ball. Place on greased cookie sheets; flatten to a 3-inch diameter. Cover; let rise in warm place until indentation remains after lightly touching.
Preheat oven to 375°F.
Prepare egg wash: Combine water and instant minced onion; let stand while rolls are rising.
Combine slightly beaten egg and onion mixture; brush mixture on top of risen rolls. Bake for 15 to 20 minutes until golden brown. Remove from cookie sheets; cool on wire rack.