Melt butter in a large skillet over medium-high heat. Add shallot and garlic; cook and stir for 30 seconds. Add mushrooms, 1/2 teaspoon salt, and white pepper. Reduce heat to medium; cook, stirring often, until moisture has evaporated and mushrooms start to brown, about 12 minutes.
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Stir walnuts and white wine into the skillet. Cook, scraping browned bits off the bottom of the skillet, until wine has evaporated, 3 to 5 minutes. Remove from heat and let cool, 10 to 15 minutes.
Preheat oven to 400 degrees F (200 degrees C).
Season Cornish hens inside and out with remaining 1 teaspoon salt, paprika, onion powder, garlic powder, and black pepper. Open cavities gently with your fingers; stuff with mushroom mixture. Pull skin back in place to cover stuffing. Place hens breast side-up in a roasting pan.
Roast in the preheated oven, basting once or twice with juices from the pan, until an instant-read thermometer inserted into the thickest part of the thigh registers 180 degrees F (82 degrees C), about 45 minutes. Garnish with thyme sprigs.
Substitute pine nuts for the walnuts if preferred.
755.09 calories; 57.11 g protein; 13.3 g carbohydrates; 52.24 g fat; 309.91 mg cholesterol; 1028.37 mg sodium.Full Nutrition
*Percent Daily Values are based on a 2,000 calorie diet. Your daily values may be higher or lower depending on your calorie needs.
**Nutrient information is not available for all ingredients. Amount is based on available nutrient data.
(-)Information is not currently available for this nutrient. If you are following a medically restrictive diet, please consult your doctor or registered dietitian before preparing this recipe for personal consumption.