Cut each chicken breast in half and lay between two sheets of plastic wrap and pound them down to 1/2 inch thickness with a mallet or rolling pin.
In a large skillet, over medium-high heat, add 1 tablespoon butter. Season chicken with dried tarragon, salt and pepper and pan-sear on each side for about 4-5 minutes until golden. Transfer to a plate.
Heat the remaining 2 tablespoons butter and olive oil, sauté onions for about 2 minutes, then add garlic, ginger and Brussel sprouts and sauté for about 2-3 minutes until the Brussel sprouts get crispy.
Add the white wine and scrap the bottom to loosen the bites on the bottom, and allow to boil until half has evaporated. Then add the chicken broth, and zucchini, simmer for 2-3 minutes. Return chicken to the skillet and add spinach, and tarragon, simmer for about 3 minutes, long enough to soften the spinach and warm the chicken.
To thicken the sauce, mix together arrowroot and water in a small bowl, then add to the skillet. Increase heat slightly, and once thickened, then remove from heat.
Serve with rice noodles or basmati, jasmine or long grain rice.
