Score the skin of the duck breast in a diamond pattern without cutting into the meat and season generously with salt. Place the breast skin-side down in a cold frying pan and put it on medium heat. By warming slowly the fat renders and the skin becomes truly crispy, about eight minutes. Pour off the rendered fat and save it.
Turn the duck breast, fry it for another three minutes on the meat side and then let it rest for ten minutes under foil. Meanwhile, peel the parsnips, cook them until tender in fifteen minutes, drain and puree with the butter, salt and pepper until a sweet, velvety puree.
Heat a spoonful of the duck fat with the olive oil in a pan and fry the bimi with the crushed garlic for three minutes over high heat until the stems are just tender and have some colour here and there. Mix the honey with the balsamic vinegar into a thin glaze. Slice the duck breast, place it on the puree with the bimi alongside and drizzle the glaze over. Finish with thyme.