Combine sour cream and egg in a bowl. Process flour and salt in food processor until combined, about 3 seconds. Add butter and pulse until only pea-size pieces remain about 10 pulses. Add half of sour cream mixture and pulse until combined, 5 pulses. Add remaining sour cream mixture and pulse until dough begins to form, about 10 pulses.
Transfer mixture to lightly floured counter and knead briefly until dough comes together. Divide dough in half and form each half into 4 inch disk. Wrap each disk in plastic wrap and refrigerate for at least 1 hour or up to 2 days. (Dough can be wrapped tightly in plastic and foil and frozen for up to 2 months. Thaw completely at room temperature before using.
Remove 1 dough disk from refrigerator and let sit for 10 minutes. Working on lightly floured counter, roll into 12 inch round and transfer to 9 inch pie plate, leaving 1/2 inch over-hang all around. Repeat with second dish and transfer to parchment lined rimmed baking sheet. Cover both doughs with plastic and refrigerate for 30 minutes.
Pat chicken dry with paper towels and season with salt and pepper. Heat oil in Dutch oven over medium high heat until just smoking. Cook chicken until browned all over, about 10 minutes; transfer to plate. Pour fat ( you should have 2 tablespoons) into small bowl; reserve. When chicken is cool enough to handle, remove and discard skin. Add broth, chicken, and bay leaf to now empty pot and bring to a boil. Reduce heat to low and simmer, covered until breasts register 160 degrees and thighs register 175 degrees, 14 to 18 minutes. Transfer chicken to bowl. When chicken is cool enough to handle shred into bite-size pieces, discarding bones. Pour broth through fine mesh strainer into second bowl and reserve. (you should have about 2 3/4 cups); discard bay leaf.
Adjust oven rack to lowest position and heat oven to 450 degrees. Heat butter and reserved fat in now empty pot over medium high heat until shimmering. Add flour and cook, whisking constantly, until golden, 1 to 2 minutes. Slowly whisk in 2 cups of reserved broth and half and half and bring to boil. Reduce heat to medium low and simmer gravy until thickened and reduce to 1 3/4 cups, 6 to 8 minutes. Season with salt and pepper to taste. Combine 1 cup gravy with chicken; reserve remaining gravy for serving.
Transfer chicken mixture to dough-lined pie plate and spread into even layer. Top with second dough round, leaving at least 1/2 inch overhang all around. Fold dough under itself so that edge of fold is flush with outer rim of pie plate. Flute edges using thumb and forefinger or press with tines of a fork to seal. Cut four 1 inch slits in top. Brush pie with egg and bake until top is light brown, 18 to 20 minutes. Reduce oven temperature to 375 degrees and continue to bake until crust is a deep golden brown, 10 to 15 minutes. Let pie cool on wire rack for at least 45 minutes.
When ready to serve, bring remaining 3/4 cup reserved gravy and remaining 3/4 cup reserved broth to a boil in saucepan. Simmer over medium low heat until slightly thickened, 5 to 7 minutes. Season with salt and pepper to taste.
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|Serving Size: 1 Serving (555g)|
|Recipe Makes: 8 Servings|
|Calories from Fat: 843 (62%)|
|Amt Per Serving||% DV|
|Total Fat 93.7g||125 %|
|Saturated Fat 34.4g||172 %|
|Monounsaturated Fat 35.4g|
|Polyunsanturated Fat 16.1g|
|Cholesterol 458.3mg||141 %|
|Sodium 350.6mg||12 %|
|Potassium 958.7mg||25 %|
|Total Carbohydrate 30.7g||9 %|
|Dietary Fiber 1.1g||4 %|
|Sugars, other 29.6g|
|Protein 91.9g||131 %|
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Calories per serving: 1355
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