Select sous vide mode and set the temperature to 145°F and time for 1 hour.
Prepare the brown butter. In a small saucepan over medium, heat butter and cook until lightly browned - 3 to 4 minutes.
Add the herbs and garlic, reduce heat to low and cook for an additional 2 minutes. Strain about 4 tablespoons of the butter into a small bowl and reserve. Strain the remainder into a separate container to reserve for serving.
Prepare the chicken. In a small bowl, combine kosher salt and sugar. Season chicken breasts generously with the salt mixture.
Using the reserved 4 tablespoons of brown butter, brush each chicken breast with about 1 tablespoon of butter. Place each chicken breast in a sous vide-safe bag. Vacuum tightly and seal.
Prepare the asparagus. Place all of the asparagus, olive oil and salt to a sous vide-safe bag. Vacuum tightly and seal.
When the water reaches set temperature, add chicken and asparagus to the water bath and press start.
When the cooking time has ended, remove bags from water bath and open.
Pat the chicken breasts dry with paper towels
In a large skillet over medium-high, heat vegetable oil. When oil begins to shimmer, add chicken to pan skin-side down. Sear chicken until skin is crispy and browned. Turn chicken and sear the other side until browned. If desired, slice chicken before plating.
To serve, warm the reserved brown butter. Place asparagus on plates and top with chicken. Drizzle with brown butter.