Dissolve yeast and sugar in 3/4 cup warm milk in a large bowl, and let sugar mixture stand 5 minutes. Add 2 cups flour, potato mixture, margarine, salt, vinegar, and egg, and beat mixture at medium speed of a mixer until smooth. Stir in 1 cup flour to form a sticky dough. Turn dough out onto a lightly floured surface. Knead dough until smooth and elastic (about 10 minutes), and add enough of the remaining flour to prevent dough from sticking to hands.
Place dough in a large bowl coated with cooking spray, turning to coat top. Cover dough, and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in bulk.
Punch dough down, and divide in half. Working with one portion at a time (cover remaining dough to keep from drying), roll dough into a 10 x 7-inch rectangle. Cut dough crosswise into 20 (7-inch-long) 1/2-inch-wide strips. Gently twist strips of dough. Repeat with remaining dough. Place dough twists 1 inch apart on two baking sheets coated with cooking spray. Cover dough twists, and let rise in a warm place (85°), free from drafts, 30 minutes or until doubled in bulk.
Preheat oven to 350°.
Uncover breadsticks. Bake breadsticks at 350° for 18 to 20 minutes. Remove from pan, and let cool on wire racks.
Note: To make 2 loaves instead of breadsticks, roll each portion into a 10 x 7-inch rectangle on a lightly floured surface. Roll up rectangle tightly, starting with a long edge and pressing firmly to eliminate air pockets; pinch seam and ends to seal. Place roll, seam side down, in a 9 x 5-inch loaf pan coated with cooking spray. Cover and let rise 45 minutes or until doubled in bulk. Bake 30 minutes or until loaves sound hollow when tapped. Remove from pans; let cool on wire racks.
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