Prepare and measure every ingredient. Cut off and keep the lemongrass top. Peel the bottom 3 inches to the pale core, trim the bulb end, and smash the tender bottom piece. Slice the vegetables and set out the finishing ingredients.
Put the chicken meat stock, chicken thighs, sea salt, both lemongrass pieces, and ground ginger if using it into the stockpot. Bring to a bare simmer, lower the heat, cover, and cook gently for 20 minutes.
Remove the lid, add the sliced vegetables, and keep the same quiet simmer for 10 minutes. The zucchini should soften without collapsing, mushrooms should darken, and celery should keep its shape.
Lift the chicken to a clean wooden board and cut the thickest piece to verify it is opaque throughout. Cut all chicken into bite-size pieces. Remove and discard both lemongrass pieces.
Return the chicken to the pot and turn off the heat. Stir in the homemade coconut milk, green onions, lime juice, fresh ginger if using it, coconut aminos, fish sauce, and optional honey. Warm through without returning the soup to a simmer.
Ladle into bowls and garnish with cilantro or mint. Add the optional diced fresh cucumber at the table.