1. In skillet, heat butter. Add onion; cook over medium heat 5 minutes. Reduce heat to low. Sprinkle with 2 teaspoons sugar; cook 20 minutes, until onions are very soft and lightly browned. Remove from heat.
2. In bowl, combine 1 teaspoon sugar, the water and yeast. Let stand 5 minutes, until foamy, to dissolve yeast.
3. In medium-size bowl, mix 2 cups flour, salt and remaining sugar.
4. Stir buttermilk, butter, onion and flour mixture into yeast mixture. Stir in 1-1/4 cups flour. Knead until smooth and elastic, 5 minutes, adding flour as needed to prevent sticking.
5. Place dough in large greased bowl; turn dough to coat. Cover with clean kitchen towel; let rise in warm place until doubled in volume, 1 hour.
6. Punch down dough. Let rest 5 minutes. Coat 2 large baking sheets with cooking spray. Divide dough into 6 equal pieces. Roll 1 piece into 20-inch long rope. Cut rope into 4 equal pieces. Roll each piece into 8-inch-long rope. Tie each into knot. Transfer knots to baking sheet. Repeat process for a total of 24 rolls.
7. Cover with clean kitchen towels. Let rolls rise in warm place 45 minutes or until doubled in volume.
8. Heat oven to 375 degrees F. Uncover pans. Brush risen rolls with egg white.
9. Bake in 375 degrees F oven 8 minutes. Rotate pans. Bake 10 to 12 minutes, until rolls are lightly browned. Transfer rolls to wire rack; let cool slightly. If baking ahead, warm before serving.