Heat large skillet over medium high heat, and add 2 tablespoons butter or ghee.
Season chicken generously with salt and pepper and place in hot pan. Don't crowd the chicken, if the pieces won't fit in an even layer, cook in two batches. Sauté chicken until browned on first side, about 5 minutes. Flip and continue cooking until browned and cooked through on second side, another 5 minutes. Remove chicken from skillet, set aside, and cover with foil.
Reduce heat to medium and melt an additional 1 tablespoon of butter or ghee. Add diced onions and cook until soft and nearly translucent, 6-8 minutes, stirring occasionally.
Stir in sliced mushrooms and cook until soft, another 6-8 minutes. Add in minced garlic and stir until fragrant, about 30 seconds.
Reduce heat to low to keep the mixture warm.
While your vegetables are cooking, make your roux. Heat a separate skillet on medium, and melt 1/4 cup butter or ghee. Once melted, and flours and whisk constantly until lightly toasted and fragrant, about 2 minutes. Stir in coconut milk or heavy cream, whisking constantly until incorporated.Bring mixture to a boil then reduce heat to medium low to maintain a simmer.
Add wine, season with salt and pepper, and whisk to incorporate. Simmer until sauce thickens, stirring frequently, about 10-15 minutes. When the sauce coats the back of spoon, it's ready.
Transfer the sauce and half of your cooked mushrooms and onions to a high-powered blender or food processor. Blend until creamy and vegetables are incorporated.
Return the blended sauce to your large sauté pan with remaining mushrooms and onions, and stir to combine.
Nestle chicken in the sauce and heat over medium low until warm throughout.
Sprinkle parsley on top and serve immediately.