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1
Pull off and discard turkey skin; rinse thighs and pat dry.
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2
In a 4- to 5-quart nonstick pan over medium-high heat, melt butter. Add turkey thighs in a single layer and turn often until browned on all sides, 4 to 5 minutes total. Transfer turkey to a rimmed plate.
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3
Meanwhile, peel garlic cloves. Add to butter in pan; stir often until lightly browned, 2 to 3 minutes. Add mushrooms, celery, and chilies; stir often until vegetables are lightly browned, 8 to 10 minutes. Add turkey and any accumulated juices, broth, and wine. Bring to a boil; cover, reduce heat, and simmer until turkey is very tender when pierced, 1 1/4 to 1 1/2 hours. Remove from heat and return turkey to rimmed plate. When turkey is cool enough to handle, pull meat from bones, tearing it into bite-size pieces; discard bones. Return meat to pan and stir in 1/2 cup minced cilantro.
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4
Meanwhile, in a bowl, mix flour, baking soda, and 1/2 teaspoon salt. Add egg and milk; stir with a fork just until dough is evenly moistened and holds together.
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5
Return turkey mixture to high heat; when boiling, reduce heat to simmering. Gently drop 2-tablespoon scoops of dough into pan in a single layer. Cover and simmer, without stirring, until dumplings are no longer moist in the center of the thickest part (cut to test), about 10 minutes.
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6
Spoon turkey and dumplings into wide bowls. Sprinkle evenly with remaining 1/4 cup minced cilantro. Add salt to taste.
