Preheat oven to 400º Fahrenheit.
Grease a 9” round baking pan.
For the chicken filling:
Heat a large skillet over medium high heat.
Melt butter in the skillet.
When butter has melted and is no longer foaming, add the diced chicken to the pan.
Cook chicken, stirring occasionally, until chicken begins to brown on all sides, but is not yet cooked throughout.
Add onion and carrots to the skillet.
Sprinkle mixture lightly with salt and pepper.
Turn heat to medium low.
Cook, stirring occasionally until the onions begin to brown at the edges, but are not yet tender.
Stir in garlic and dried thyme.
Cook one minute, stirring constantly.
Stir in vinegar, scraping up browned bits.
When vinegar has almost completely evaporated, stir in broth.
Turn heat to medium high Simmer broth, stirring occasionally until it thickens, about 15-20 minutes.
The broth is thick enough when you can “draw” a line on the bottom of the pan with a spoon, and the line does not immediately fill in.
While the filling simmers, prepare the biscuit topping.
Once the broth has thickened, add heavy cream and peas.
Bring mixture to a simmer.
Turn heat to low.
Simmer until mixture is thick and gravy-like.
Taste before adding salt and pepper.
Season to taste with salt and pepper, if necessary.
For the topping:
In a medium mixing bowl, whisk together the almond flour, ground flax seeds, xanthan gum, baking powder, and salt.
Cut the butter into the dry ingredients using a pastry blender.
Mixture should appear mealy.
In a small bowl, whisk the sour cream and the egg white together.
Stir this mixture into the dry ingredients.
Gather mixture into a ball and place on a piece of parchment paper or a counter dusted with almond flour.
Using clean hands or a rolling pin dusted with almond flour, press or roll dough into a circle about 8 inches in diameter.
To assemble:
Pour chicken filling into the prepared baking dish.
Gently place biscuit dough over the chicken filling.
Bake in preheated oven for 10-12 minutes, or until biscuit topping has browned.