Melt the butter until slightly foaming in a heavy pan over medium-high heat.
Sear the chicken thigh until golden brown, about 4-5 minutes on each side. Remove from pan and set aside.
In the same pan, turn down the heat to medium and sautee the garlic, about 1 minute.
Add the mushrooms and stir occasionally to prevent burning, about 3-4 minutes.
Add the chicken stock and lemon juice and deglaze the pan, scraping up any brown bits.
Turn off heat and add double cream and parmesan cheese. Return to medium heat and whisk sauce until well-combined. Bring the sauce to boil, then reduce to an energetic simmer.
Add the chicken to the pan, simmer for 5-6 minutes and flip over, simmer for another 5-6 minutes.
Add the asparagus to the pan, simmer for another 5 minutes (I like to add the asparagus at the end for a tender crisp finish).
Season with salt and pepper, to taste.
Garnish with chopped parsley.