In a saucepan, add parsnips, milk, butter, salt, and pepper. Bring to a boil. Reduce heat to low. Simmer, covered until parsnips are soft.
Removed from heat. Using a blender, purée the milk and parsnip mixture until creamy and smooth, about 2 to 3 minutes.
Add oil and rosemary to a sauce pan. Simmer over low heat until fragrant. Let cool 10 minutes before using.
Garnish with 1 to 2 tablespoons of rosemary oil and fresh rosemary.