Heat oil in large skillet set over medium heat; cook shallots and red pepper flakes for 5 minutes or until softened.
Stir in butternut squash, salt and pepper. Cook, stirring occasionally, for 5 to 7 minutes or until squash starts to brown.
Stir in broth, butter, vinegar and honey.
Cover; cook for 10 minutes or until liquid is absorbed and squash is tender.
While this is cooking, simmer some water, stir in a circular direction. Crack an egg into a bowl without breaking the yolk. Pour into the simmering water, trying to pour the white in first. Cook for 2 minutes, no more, then transfer to a paper towel plate and repeat.
Once the eggs are done and the hash is done, plate, and garnish with chives.