Pat the chicken breasts dry with a paper towel and season both sides evenly with sea salt and black pepper.
Heat the olive oil in a large stainless steel or cast-iron skillet over medium-high heat until shimmering.
Place the chicken in the skillet and sear for 5-6 minutes per side until golden brown and cooked through; remove chicken from the pan and set aside to rest.
In the same skillet, add the ghee and sliced cremini mushrooms, sautéing for 4 minutes until they release their moisture and begin to brown.
Add the finely minced shallot and garlic to the mushrooms, stirring constantly for 1 minute until fragrant.
Pour in the chicken broth and coconut aminos, using a wooden spoon to scrape up the flavorful brown bits from the bottom of the pan.
Stir in the fresh thyme and let the sauce simmer for 3 minutes until slightly reduced and glossy.
While the sauce simmers, steam or quickly pan-fry the asparagus spears in a separate small pan with a splash of water until vibrant green and crisp-tender.
Slice the rested chicken and plate it alongside the asparagus, spooning the savory mushroom sauce generously over the top.