Prep the vegetables:
Combine 4 quarts water and 1/4 cup kosher salt in a large pot and bring to a boil over high heat. Meanwhile, trim most of the stem off the broccoli to separate the florets. Using a small, sharp knife, trim the stem of each floret so it’s 1-1/2 to 2 inches long. Starting at the top of the stem (just beneath the tiny buds), cut through the stem lengthwise and divide the floret in half—preferably without using the knife to cut through the flowery buds. Repeat the process, dividing each floret into two to four pieces, until the top of each floret is about the size of a quarter. Have ready a bowl of ice water. Boil the florets until they turn bright green, about 1 min. Drain the florets in a colander and then plunge them into the ice water to stop the cooking and set the broccoli’s color. Drain again.
Trim the carrot tops, but leave about 1-1/2 inches of the green tops intact. Peel the carrots and cut them lengthwise into halves, quarters, or sixths, depending on the size.
Remove the tough outer celery ribs; reserve for another use. Trim the tops of the ribs and about 1-1/2 inches from the root end. Starting with the large ribs, cut each lengthwise into long, thin sticks about 1/4 inch wide. Trim the large leaves from the celery heart and cut each rib in the same manner, preserving as much of the tender leaves as possible.
Discard the outer leaves of the radicchio. Trim the root end and cut the radicchio in half through the core. Cut each half into 1/4-inch-thick wedges—the core should hold each wedge intact. Trim any stalks from the top of the fennel bulb and cut it in the same manner as the radicchio, but don’t discard the outer layers unless they’re discolored.
Trim the tops of the radishes, leaving about 1 inch of the green tops. (If the leaves are especially nice, leave a few intact for garnish.) Quarter each radish lengthwise.
Store the vegetables:
Refrigerate the vegetables in separate sealed containers or zip-top bags. When ready to serve, arrange the vegetables on a large platter or in a shallow basket. Mist the crudités lightly with water to keep them looking fresh. Serve with the dip on the side.
Store the prepped vegetables in separate airtight containers so they stay crisp.