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1
Position a rack in the lower third of the oven and preheat the oven to 375F.
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2
Place the carrots, celery, onion, and garlic in a large Dutch oven and season with salt and pepper.
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3
Bake the vegetables, uncovered, stirring them once or twice, until they are tender and browned, about 1 hour.
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4
Transfer the Dutch oven to the stove top.
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5
Add the stock and 3 cups of warm water and bring to a boil over high heat.
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6
Add the bay leaves and turkey giblets and neck.
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7
Reduce the heat to low and let simmer until the liquid is reduced to about 3 cups, 1 to 1 1/2 hours.
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8
Strain the stock through a sieve into a medium-size saucepan, pressing hard on the solids to extract all the liquid.
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9
Discard the solids.
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10
If you are planning on adding the turkey pan drippings, refrigerate the reduced stock, covered, until you are ready to proceed.
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11
Place 1 cup of the strained stock in a medium-size bowl and add the half-and-half and flour.
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12
Whisk until smooth.
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13
Place the saucepan with the remaining stock over high heat and bring to a boil (see Notes).
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14
Stir in the flour mixture.
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15
Reduce the heat to low and let simmer, whisking frequently, until the gravy thickens and the raw taste of the flour cooks off, about 15 minutes.
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16
If the gravy is too thick, add more half-and-half or water.
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17
If it is not thick enough, add 1/2 to 1 tablespoon more flour and let the gravy cook for 3 to 5 minutes longer.
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18
Taste for seasoning, adding more salt and/or pepper, as needed.
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19
If you are not planning on serving the gravy immediately, transfer it to a clean container and let it cool.
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20
The gravy may be refrigerated, covered, for up to 2 days.
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21
Reheat over medium-low heat.
