Pulse all dressing ingredients in a food processor till fully blended. Taste and adjust-- if it's too tart for your tastes, add more oil, but the acid spreads well on the fresh veggies.
Using either a julienne peeler or a Spiralizer, turn your zucchini into noodles (cut them occasionally so you don't end up with a Lady & the Tramp length noodle!) Finely sliced or julienne your carrot, the pepper and the cabbage.
Two options: either serve it cold by just tossing the whole thing with just enough dressing, chilling for an hour, and topping with your choice of garnishes. Or, you can quickly stir fry all the veggies in some melted oil and top with the dressing while still warm.