Lightly spoon flour into measuring cup; level off. In large bowl, combine 2 cups flour, yeast, salt and pepper. In small saucepan, heat water, oil and honey until very warm (120 to 130°F.).
Add warm liquid to flour mixture; blend at low speed until moistened. Beat 3 minutes at medium speed. Stir in egg yolk and enough of the remaining flour until dough pulls away from sides of bowl. (Dough will be soft.) Cover; let rise in warm place (80 to 85°F.) for 40 minutes or until doubled in size.
Heat oven to 400°F. Generously grease cookie sheets. Punch down dough. On floured surface, knead Cheddar cheese into dough. Divide dough into 12 pieces. Roll each piece into pencil-thin 18-inch rope; tie in loose pretzel shape. (See diagram.) Place on greased cookie sheets. Brush with egg white; sprinkle with Parmesan cheese.
Bake at 400°F. for 12 to 18 minutes or until golden brown. Immediately remove from cookie sheets. Cool completely on wire racks.