In a large, high-sided skillet over medium-high heat (about 6-7 out of 10), heat garlic-infused olive oil. Season chicken thighs with salt and pepper on both sides.
Once oil is shimmering, brown chicken thighs on each side for 5-7 minutes. Chicken should be almost cooked through. Remove from pan and set aside.
In the same skillet back on the stove on medium, melt butter. Add carrots, sweet potato and celery. Cook, stirring frequently for 5 minutes.
After 5 minutes, add kale, canned mushrooms & green onion tips. Cook for an additional 2 minutes.
Add dry white wine, scraping up the bottom bits from the pan. Allow this to simmer and reduce by half, about 4-6 minutes.
Add 1½ cups of chicken broth, coconut milk, parsley and thyme. Bring to a gentle simmer.
Place chicken thighs back in the skillet, ensuring to submerge most of the thigh in the liquid. Continue to simmer for 10 minutes, until chicken thighs are cooked through.
During the last minute, give the remaining ¼ cup chicken stock + arrowroot mixture a stir to evenly distribute the arrowroot flour, and add into the skillet to thicken the sauce.
As the salt content could vary depending on your butter, adjust with additional salt and pepper to taste before serving.