In food processor fitted with chopping blade, process 2½ cups flour, the cheese, milk powder, yeast, salt, sugar, and ¼ teaspoon red pepper just until mixed. In cup, combine water and oil.
With processor motor running, slowly add water mixture through feed tube. Process until dough pulls away from side of container.
Let dough stand in processor 5 minutes. Meanwhile, oil a large bowl. Reprocess dough 20 to 30 seconds and transfer to oiled bowl. Cover with plastic wrap. Let rise in warm place, away from drafts, until double in size -- about 40 minutes.
Divide dough into 2 balls and dust with flour; set aside 5 minutes.
Meanwhile, grease or coat with nonstick vegetable cooking spray 3 large baking sheets. On floured surface, with floured rolling pin, roll each half into a 12- by 10-inch rectangle. (If dough is too elastic and difficult to roll out, set it aside to relax and roll out other half.)
Brush rectangle surface with egg-white mixture and sprinkle generously with paprika. Lightly sprinkle with some red pepper. With floured pizza-cutting wheel or sharp knife, cut rectangle crosswise into 4 smaller rectangles; cut each rectangle lengthwise into six 10-inch-long strips, making 24 strips in all.
Gently pick up both ends of each strip and twist 3 or 4 turns in opposite directions. Place twisted strips, 1 inch apart, on greased sheets, pressing ends into sheet to keep them from untwisting. Let strips rise 15 minutes or until puffy. Repeat Steps 4 and 5 with other half of dough.
Heat oven to 375º F. Bake strips 15 minutes or until crisp and lightly browned. Cool sticks on wire racks. Store in airtight containers.