Place eggs in a small pot and cover with water. Heat over high. Once boiling, turn off heat and allow eggs to sit for 10 minutes. Rinse in cold water, peel and place in a bowl to cool.

Meanwhile, cut cucumber into 1 1/2 inch thick pieces, removing the ends so that all pieces are able to sit on a flat surface. Using a melon baller or small spoon, scoop out the center of the cucumbers, enough to be filled.

Mash eggs with mayonnaise, mustard, salt, pepper and paprika. Fill cucumber cups with egg salad.

Peel and cut carrot into small sticks. Serve with cucumber cups.