Blanch dandelion greens in a pot of boiling salted water.
Drain and squeeze out excess water, chop, and set aside.
Heat olive oil in a large pot over medium-high heat.
Add greens, carrot, and leeks and cook, stirring often, for 15 minutes.
Add vegetable stock and simmer for about 15 minutes.
Reduce heat to medium and whisk in milk.
Cook, stirring frequently until slightly thickened.
Add Dijon mustard and purée mixture in a blender until smooth.
Season with salt and pepper to taste.