In a large pan of boiling salted water cook the carrots until barely tender, 2 to 3 minutes.
Remove the carrots with a slotted spoon, reserving the water, and rinse under cold running water to stop the cooking.
Reserve in a bowl.
Separate the cauliflower into small florets.
Bring the same pan of water to a boil, adding more water if needed, and cook the cauliflower, uncovered, until crisp-tender, about 3 minutes.
Drain and rinse under cold running water to stop the cooking.
Drain again and put into a large bowl.
In a small bowl mix the mayonnaise, sour cream, mustard, lime juice, salt, and pepper.
Add to the cauliflower and stir gently to mix.
Arrange the cauliflower on a round serving platter.
Sprinkle with parsley.
Arrange the carrots around the cauliflower.
Serve cold or at room temperature.