Prepare a large pot of boiling salted water, and fill a large bowl with ice water.
Remove the tough bottoms of the asparagus stalks. If they are thick, peel the stems half-way up the stalk.
Add the carrots to the pot of boiling water and blanch for 1 minute. Immediately remove the carrots with a slotted spoon and plunge them in the bowl of ice water. Drain the carrots when fully cooled.
Add the asparagus to the boiling water and blanch for 1 minute. Immediately remove the asparagus with a slotted spoon and plunge them into the reserved bowl of ice water. Drain the asparagus when fully cooled.
Slice the radicchio into wedges.
Arrange the carrots, asparagus, cherry tomatoes, and radicchio on a platter and serve with the Herb Dip.
Place the cream cheese, sour cream, mayonnaise, scallions, parsley, dill, salt, and pepper in the bowl of an electric mixer fitted with the paddle attachment and blend. Serve at room temperature.