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Combine all of the dough ingredients, and mix and knead them, by hand, mixer, or bread machine, to make a smooth dough.
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Place the dough in a bowl or rising container, cover it, and let it rise for 60 to 90 minutes, until it's just about doubled in bulk.
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Gently deflate the dough, and divide it into six pieces.
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Round each piece into a ball.
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Stagger the balls on a lightly greased or parchment-lined baking sheet. Cover, and let rise for about 1 hour.
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The balls should become quite puffy. Towards the end of their rising time, preheat the oven to 350°F.
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Bake the buns till they're a deep, golden brown, about 25 minutes. Remove them from the oven, and let them cool right on the pan.
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When you're ready to make bread bowls, cut the top 1/3 off each bun.
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Gently and carefully scoop out the bread inside. Reserve it to make herb-flavored crumbs, if desired.
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Place the bread bowls on a baking sheet or platter, and set them aside while you make the filling.
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Melt the butter in a heavy saucepan and add the flour, stirring to combine.
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Slowly add the broth in a stream, stirring constantly to keep the mixture from becoming lumpy. If it does get lumpy, just keep stirring till it smooths out.
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Add the half and half or milk, stirring till smooth. Bring just to a boil, then simmer gently, stirring frequently, for 5 minutes.
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Add the chicken or turkey, salt, thyme, and sherry, stirring to combine.
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Add the cooked, drained vegetables, stirring to combine.
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Bring the mixture just to a simmer, and immediately spoon a generous 1/2 cup into each bread bowl. Serve immediately.