Bring a pot of salted water to a boil. Add the potatoes and cook until just tender, about 10 minutes depending on how large you cubed them. Remove from heat and remove potatoes from the water and let cool. (I poured the potatoes into a colander, but kept an inch or two of water in the pot.)

Return the pot to the stove and bring to a boil again. Add the carrots and cook 3 minutes. Drain completely and let cool.

Heat the oil in a large skillet. Add the sausage slices and cook over medium high heat for 5 minutes until they get golden brown. Remove to a paper towel-lined plate and let cool.

In a large bowl mix the mayonnaise, mustard, cayenne, and parsley.

Add the potatoes, carrots, sausage, olives, and radishes. Season with salt and pepper and gently fold to combine.

Cover and refrigerate 30 minutes.

Serve garnished with more chopped fresh parsley.