Bring a large quantity of salted water to a boil. Fill another bowl with water and add ice. Add the parsley to the boiling water and blanch until softened, about 2 minutes. Transfer to the ice water. When cold, drain and squeeze the parsley well to remove as much water as possible. Transfer to a blender and add the salt and sugar. Start the machine, and add the oil in a thin, steady stream. Blend until the blender jar feels slightly warm, 3 to 5 minutes.
To make the parsnips, combine them and the garlic in a large saucepan, then add water to cover and a pinch of salt. Bring to a boil, reduce the heat, and simmer until the point of a knife inserted into the parsnips meets no resistance, about 25 minutes. Drain, transfer to a food processor, and puree. Add the honey and butter and season with salt and pepper to taste. Pulse to blend. Keep warm.
To make the venison, combine the fennel, coriander, cardamom, and black pepper on a large plate and mix. Season the venison with the salt to taste and roll it lightly in the spice mixture to coat evenly.
Heat a large skillet over high heat. Add the oil and swirl to coat the pan. Add the venison and sear it, turning once, about 8 minutes for medium-rare. Allow the meat to rest for 5 minutes, then slice into 6 pieces each.
PLATING: Divide the puree among 4 serving plates. Surround each portion with 3 upright pieces of the venison, drizzle over the parsley oil, and serve.