For radish roses, trim both ends of each radish. With a sharp paring knife, make small rounded cuts toward bottoms, leaving them attached to the base. Make similar petal-shaped cuts above and behind the base cuts to resemble a blooming rose. Place in ice water.
Cut white portions of onions into 1-1/2-in. lengths; set aside green portions of onions for flower stems. Cut white portions into thin strips, leaving one end intact. Add to ice water. Refrigerate until radishes open and onions are curled, about 30 minutes.
Meanwhile, cut top off of pumpkin; scoop out and discard seeds. Place cabbage half in pumpkin, flat side down, for base.
Score cucumber by cutting lengthwise strips through peel; cut cucumber into slices. Thread the cucumber, cauliflower and broccoli onto skewers; insert into cabbage base. Drain radishes and onions; thread onto skewers and insert into base.
For carrot tulips, make cuts with a paring knife down the sides of carrots toward the base. Thread green beans and reserved green onion portions onto skewers. Top with carrot tulips and tomatoes. Insert into base. With toothpicks, attach asparagus to base. Fill in around inside edge of pumpkin with parsley sprigs.