Stir the chicken stock, water, and lemon juice in a large pot with the onion, garlic, ginger, and parsnips. Season with thyme, red pepper flakes, salt, and pepper. Bring to a simmer over medium-high heat, and cook until the parsnips are tender and the onions are translucent, about 10 minutes.
Remove and discard the thyme sprigs. Stir in the honey to your desired level of sweetness. You don't want the broth too sweet. Lower the heat to a gentle simmer, and stir in the walleye and bean sprouts. Cook gently for 5 minutes, then add the basil and green onion. Continue cooking until the fish is flaky and opaque, about 5 minutes more. Season to taste with salt and pepper. Garnish with mint leaves to serve.
