Blend the basil, vinegar, 1 teaspoon of salt, and 1/2 teaspoon of pepper in a blender
. With the machine running, gradually blend in the oil.
Place the arugula and radicchio
in a wide shallow bowl. Using a vegetable peeler
, shave the carrot over the salad. Shave the cucumber into a medium bowl. Pat the cucumber shavings with paper towels to absorb the excess moisture. Add the cucumbers
to the salad.
Do-Ahead Tip: The vinaigrette
and salad can be prepared 1 day ahead. Cover separately and refrigerate. Whisk
the dressing to blend before using.
Toss the salad with enough dressing
to coat. Season the salad, to taste, with salt and pepper, and serve.