Melt butter in 12-inch skillet over medium heat. Cook frozen onions in butter about 10 minutes, stirring occasionally, until water from onions is reduced and onions begin to soften.
Stir vinegar and sugar into onions. Cook, stirring constantly, until sugar is dissolved; reduce heat. Simmer uncovered about 10 minutes, stirring occasionally, until liquid is reduced to a glaze consistency. Sprinkle with salt and pepper. Garnish with parsley.