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1
For dough, put yeast, sugar, salt, 3 cups flour, water, eggs and butter in mixing bowl.
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2
Beat on high for 3 to 5 minutes, until very smooth.
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3
Using a wooden spoon, stir in 3 cups flour.
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4
Add flour 1/2 cup at a time until dough becomes too stiff to stir.
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5
Turn out onto work surface and continue to add remaining flour, kneading, until dough is smooth, 7 to 10 minutes.
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6
(Use last 1/4 cup flour only if needed to prevent sticking.) Grease large bowl.
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7
Add dough, turning to coat.
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8
Cover and leave in warm place until doubled in bulk, about 1 1/2 hours.
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9
For onions, melt butter in skillet over low heat.
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10
Add onions, garlic, salt and pepper.
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11
Cover and cook, stirring often, 10 to 12 minutes or until very soft.
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12
Sprinkle in sugar.
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13
Increase heat to medium-low.
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14
Stir until onions are very brown but not scorched (2-3 minutes).
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15
Add Worcestershire, scrape up browned bits and simmer, stirring until juices evaporate.
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16
Cool.
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17
To make buns, punch down dough and knead in onions until evenly distributed.
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18
Divide and roll into 10 smooth round buns.
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19
Place on 2 baking sheets lined with parchment paper.
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20
Cover and let rest 30 minutes.
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21
For glaze, whisk egg whites with water and brush over each bun.
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22
Bake buns in two batches in the centre of a preheated 375u00b0F oven for 20 to 22 minutes, until golden brown and tops start to sound hollow when tapped.
