In a large bowl, combine chicken thighs, mustard, 1 tablespoon olive oil, 1 teaspoon salt, and 1/2 teaspoon black pepper. Toss well with your hands, smearing the mustard and seasonings evenly over both sides. Set aside or refrigerate up to 3 hours.
Heat 1 tablespoon olive oil and 1 tablespoon butter over medium heat in a 12 inch skillet. Add the chicken thighs to the skillet and cook until browned on the first side, about 4 to 5 minutes. Flip and continue cooking until browned and cooked through, about 4 minutes longer, or until 165° F in the thickest parts. Turn down the heat if the fond on the bottom of the pan starts to burn. Transfer the thighs to a plate and set aside, leaving the fat in the pan.
Add the asparagus, garlic (if using), lemon zest, and season with salt and pepper. Sauté for 2 to 3 minutes, stirring often, or until the asparagus is bright green and starting to soften (the time will depend on the thickness of your asparagus).
Add the rosé and simmer until reduced by half (about 1 minute) then add the miso and 1 tablespoon butter, stirring until they’re completely dissolved and integrated. Add additional wine/vermouth, stirring to form a nice sauce, and return chicken thighs to the skillet, along with any juices that accumulated on the plate. Simmer until the sauce slightly thickens and the chicken is just warmed through. Adjust acidity and seasoning with lemon juice and salt, to taste. Serve warm over couscous, pasta, or rice.