In a small saucepan combine carrot juice, brown sugar, walnuts, cinnamon, ginger, nutmeg, and salt.
Heat gently and stir until the sugar dissolves.
Bring to a soft simmer and cook for 5–6 minutes to infuse the walnut and spices.
Remove from heat and stir in vanilla extract.
Let cool slightly, then fine strain out the walnuts.
Bottle and refrigerate. Keeps about 2–3 weeks.