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1
Preheat oven to 325, then cook the onions and carrots on the stovetop (in a casserole just large enough to hold the whole chicken) in 2 T butter until vegetables are tender but not brown.
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2
Rub the outside of the bird with 1.5T of the butter and place the other 1.5 T inside the bird.
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3
Sprinkle the outside with half of the salt and tarragon and the inside with the other half.
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4
Truss and arrange the chicken breast-side-up on top of the sauteed vegetables in the casserole.
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5
Pour the wine into the casserole and add enough of the chicken broth to reach about 1/3 of the way up the chicken.
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6
Add the herbs and giblets.
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7
Bring to a simmer on top of the stove.
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8
Drape the damp cheesecloth over the breast and thighs.
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9
It should be long enough to fall into the liquid on either side so that is will draw the broth over the chicken and basted it during the cooking.
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10
Smear remaining butter over cheesecloth and top with a layer of waxed paper.
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11
Cover casserole and set in the preheated oven.
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12
Bake chicken for 1 hour and 40 minutes.
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13
Watch to make sure that the liquid remains at a very soft simmer and adjust temperature accordingly if needed.
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14
When chicken is done (juices should run clear), remove chicken to a platter and strain the cooking juices.
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15
Return one cup of the stock to the casserole with the chicken.
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16
Cover to keep warm while you prepare the sauce.
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17
For sauce: Melt butter in saucepan, blend in flour with a wooden spoon and stir over moderate heat until butter and flour foam together for 2 minutes without browning.
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18
Remove from heat and as soon as it stops bubbling, add 2 cups of the hot chicken stock,, blending vigorously with a wire whisk.when smooth, set over moderate heat and stir slowly as sauce thickens and comes to a boil.
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19
Boil, stirring for 2 minutes.
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20
Sauce will be quite thick.
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21
Pour in 1/3 cup of the cream and add successive spoonfuls until sauce thins out but is still thick enough to lightly coat a spoon.
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22
Check seasoning and add salt, white pepper and lemon juice to taste.
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23
Just before serving beat in the remaining 2 T butter.
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24
Carve the chicken and top with the sauce.
