Preheat your oven to 400°F (200°C). Pat the thick-cut chicken breasts perfectly dry and season with half the kosher salt. Heat olive oil in a large skillet over medium-high heat. Sear the chicken for 4-5 minutes per side until a deep golden-brown crust forms. Transfer the partially cooked chicken to a rectangular white ceramic baking dish.

Reduce the skillet heat to medium-low. Melt the butter and sauté the minced garlic for 30 seconds. Whisk in the all-purpose flour for 1 minute to create a roux. Slowly whisk in the chicken broth, followed by the heavy cream and remaining salt. Simmer for 3-4 minutes until it becomes a rich, opaque, thick white sauce.

Arrange the trimmed bright green asparagus spears evenly alongside the seared chicken in the baking dish. Pour the hot creamy sauce entirely over the top, smothering the ingredients while letting the golden-brown crust of the chicken peek through.

Bake in the preheated oven for 15-20 minutes. Watch for the glossy surface of the cream sauce to bubble aggressively around the edges. The dish is done when the chicken reaches 165°F (74°C) internally and the asparagus is tender-crisp.

Remove from the oven and let rest for 5 minutes so the sauce thickens. Generously speckle the surface with coarse black pepper and finely chopped green parsley flakes before serving.