Cook onion in the butter till tender but not brown; remove 2 tablespoons mixture and set aside remaining.
Prepare roll dough according to package directions, except add one of the eggs and the 2 tablespoons onion to the mixture.
Cover and let rise in warm place till double, 45 to 60 minutes.
Beat the remaining egg slightly; add 1 tablespoon of the egg mixture to the remaining onion mixture; add milk and salt.
With lightly floured hands, shape roll dough into 12 round buns.
Place on greased baking sheet and make a large indentation in center of each with fingers.
Spoon about 2 teaspoons onion mixture into each indentation.
Brush tops with reserved egg.
Cover and let rise till double, 45 to 60 minutes.
Bake in 375° oven for 20 to 25 minutes.