Remove any tough ends from the asparagus and cut the spears into 1-2-inch pieces. If using broccoli, cut the florets into bite-size pieces. Set aside.
Remove any tough, dry stems from the broccoli rabe or kale; the rest of the stems will be used. If using tatsoi, slice off the root end. Chop the broccoli rabe, kale or tatsoi, placing the florets and stem pieces in a pile with the asparagus spears. Place the chopped leaves, which will cook more quickly, in a separate pile.
In a small bowl, mix the soy sauce, brown sugar or honey, and sriracha. Set aside. (As mentioned in the notes section, if you plan to toss in pasta, you may wish to double the sauce.)
In a large (12-to 14-inch) skillet (cast iron works very well), heat 2 tablespoons of the oil, and sauté the chicken over medium-high heat until it is well browned and beginning to caramelize. Chicken thighs won’t dry out like breast meat, so you can really cook them until they are golden. Remove the chicken to a plate.
Pour the wine or broth into the pan to deglaze, scraping up all those little crusty bits on the bottom of the pan. (There’s serious flavor there!) Add the asparagus, florets and stem pieces–everything except the leaves–to the skillet. Sauté until crisp tender, 2 to 3 minutes, stirring frequently. You may add another drizzle of oil if your pan seems dry. Add the chopped leafy parts, and sauté until the leaves begin to wilt but are still bright green–this won’t take long.
Add the chicken back into the pan, and pour the sauce all over. Toss to incorporate, and cook another minute or two or until the chicken is thoroughly heated.
If desired, garnish with sesame seeds, peanuts or cashews. Serve as is or with rice or noodles.