Place the whole black peppercorns in a zip-top bag and crush them with a heavy skillet or use a mortar and pestle until they are coarsely cracked.
Season the chicken breast with sea salt and press the cracked peppercorns firmly onto both sides of the meat to create an even crust.
Heat the ghee in a stainless steel or cast-iron skillet over medium-high heat until it is shimmering and hot.
Place the chicken in the skillet and sear for 5 to 6 minutes per side until the crust is golden brown and the internal temperature reaches 165 degrees Fahrenheit.
Remove the chicken from the pan and set it aside on a plate to rest, keeping it warm.
In the same skillet, add the finely minced shallot and sauté for about 2 minutes until it becomes translucent and picks up the flavor from the pan.
Deglaze the pan by pouring in the chicken bone broth, using a wooden spoon to scrape up all the flavorful browned bits from the bottom.
Whisk in the full-fat coconut milk and Dijon mustard, then let the sauce simmer for 3 to 4 minutes until it reduces into a velvety consistency.
While the sauce thickens, steam or lightly sauté the asparagus spears in a separate pan until they are tender-crisp.
Slice the rested chicken breast against the grain, plate it alongside the asparagus, and generously spoon the warm peppercorn cream sauce over the top.