Bring 1 cup broth to a boil, add carrots and rosemary, boil 4 minutes.
Drain, reserving liquid and discard rosemary.
Blanch snap peas, drain, rinse under cold water, add to carrots.
Cut a small \"X\" in the root end of each onion, being careful not to cut too deeply, boil onions for 10 minutes, drain, rinse, peel, set aside.
Melt butter in a saucepan, add flour and cook, whisking over medium-low heat for 3 - 4 minutes.
Add reserved carrot liquid and enough broth to equal 2 cups. Cook, whisking, until thickened.
Add a sprig of rosemary, cover, set aside to cool.
Lightly butter 4 - 1 1/2 cup ramekins.
Place a portion of chicken in each, followed by a portion of the vegetables.
Pour the thickened sauce over each mixture.
Cover ramekins and place in refrigerator.
On a cool, floured surface, roll out pastry to form a 1/4\" thick rectangle.
Cut into 4 rectangles.
Whisk water and egg together, brush the outside rim of each ramekin with egg wash.
Drape pastry over top and seal edges.
Trim any excess dough and chill in freezer for 20 minutes.
Preheat oven to 475 and bake 15 to 18 minutes, until pastry is puffed and well-browned.
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