Rinse the wild rice in a fine-mesh strainer under cold water for 30 seconds, dice the onion, carrots, and celery to about ¼ inch, mince the garlic, strip the thyme, cut the turkey into ½-inch pieces, and set the half-and-half out to lose its chill. Chop the parsley and set aside.
Melt the butter in a Dutch oven over medium heat until it foams but does not brown. Add the onion, carrots, celery, and ½ teaspoon of the salt, then cook 6 to 8 minutes, stirring often, until the onion is translucent and the carrots begin to soften without browning.
Stir in the garlic and cook 30 seconds until fragrant. Sprinkle the flour evenly over the vegetables and stir constantly for about 2 minutes so the flour coats everything and loses its raw taste; the mixture will look pasty and clumped.
Pour in 1 cup of the broth and whisk firmly until smooth and thick, then add the remaining 5 cups in two additions, whisking after each so no lumps form. Scrape the bottom of the pot with a wooden spoon to release any browned bits.
Stir in the rinsed wild rice, bay leaf, thyme, and black pepper. Bring to a boil over high heat, then reduce to low, cover with the lid slightly ajar, and simmer 45 to 50 minutes, stirring every 10 minutes, until many grains have split open and the rice is tender with a slight chew. Add ½ cup extra broth or water if it looks too thick.
Stir in the diced turkey and simmer uncovered over low heat for about 5 minutes until heated through and reading 165°F (74°C) on an instant-read thermometer. Fish out and discard the bay leaf.
Turn the heat to the lowest setting so the soup stops bubbling, then pour in the room-temperature half-and-half and the dry sherry, if using. Stir gently for 3 to 5 minutes until steaming hot but not boiling; never let it return to a bubble once the dairy goes in.
Taste and stir in the remaining ¼ teaspoon salt and more pepper if needed. Rest off the heat for 5 minutes, then ladle into warm bowls, sprinkle with parsley, and thin with a splash of warm broth if you like a looser consistency.