In a large oven-safe skillet, melt the butter over medium heat. Add the chicken thighs and sear on both sides until golden brown and cooked through, about 4 to 5 minutes per side. Remove, cool slightly, and chop into bite-sized pieces.
In the same pan, add the onions, carrots, and celery. Cook for 4 to 5 minutes, stirring occasionally, until softened.
Sprinkle the flour over the vegetables and stir for about a minute until it forms a paste. Slowly pour in the chicken stock, whisking constantly.
Add the chopped chicken back into the pan. Stir in the cream, salt, pepper, sage, nutmeg, Italian seasoning, and paprika. Simmer for about 5 to 7 minutes, until the sauce thickens.
Preheat the oven to 425°F (220°C). In a large bowl, whisk together the flour, baking powder, and salt. In a separate bowl, combine the Greek yogurt, melted butter, and egg.
Pour the wet ingredients into the dry and gently mix with a fork until a soft dough forms. Don't overmix.
Using an ice cream scoop or two large spoons, drop 8 equal dollops of dough evenly over the top of the chicken mixture.
Transfer the skillet to the oven and bake for 18 to 20 minutes, or until the biscuits are puffed, golden brown, and cooked through.
Let it rest for 5 minutes before serving. Serve straight from the skillet.