Preheat your oven to 400°F and line a small baking sheet with parchment paper.
Toss the asparagus spears with 0.5 tsp olive oil and a pinch of the sea salt and black pepper, then roast for 10-12 minutes until tender.
Slice the chicken breast into two thick, round medallions (tournedos) and season both sides with the remaining sea salt and black pepper.
Heat 1 tsp olive oil in a stainless steel or cast iron skillet over medium-high heat.
Sear the chicken tournedos for 5-6 minutes per side until a golden crust forms and the internal temperature reaches 165°F.
Remove the chicken from the pan and tent loosely with foil to rest.
In the same skillet, add the sliced mushrooms and minced shallots, sautéing for 4-5 minutes until the mushrooms release their moisture and brown.
Stir in the minced garlic for 30 seconds, then pour in the chicken broth and Dijon mustard, scraping up any browned bits from the bottom of the pan.
Simmer the sauce for 2 minutes to reduce slightly, then remove from heat and whisk in the Greek yogurt and fresh thyme.
Place the chicken on a plate, spoon the warm mushroom sauce over the top, and serve alongside the roasted asparagus.