Veggie Sticks and Pesto Dipping Sauce

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4 ribs celery, cut into sticks or, store bought precut celery sticks

4 carrots, peeled and cut into sticks, or 10 ounce store bought package carrot sticks

1 large red bell pepper, seeded and cut into strips lengthwise

8 thin scallions, trimmed

1/2 zucchini, cut into sticks

1 cup basil leaves

1/2 cup flat-leaf parsley tops

1 clove garlic, cracked away from skin

1 lemon, zested and juiced

1/3 cup walnut pieces, a couple of handfuls

1/4 cup grated Parmigiano-Reggiano

1/2 cup extra-virgin olive oil, eyeball it

Salt and freshly ground black pepper