Roast tomatoes: Preheat oven to 450°F with a rack in the upper third. On a rimmed baking sheet, toss tomatoes with 1 tablespoon oil and a generous pinch each of salt and pepper. Roast on upper oven rack until lightly charred and starting to burst, about 20 minutes.
Prep ingredients: Trim ends from zucchini, then coarsely grate on the large holes of a box grater to make 1 cup. Spread on a paper towel and sprinkle with salt. Let sit for 5 minutes, then squeeze out any excess moisture. Peel and finely chop 2 teaspoons garlic. Finely grate Parmesan. Drain and rinse white beans. Thinly slice chives
Mix & form fritters: In a medium bowl, use a potato masher or fork to coarsely mash beans. Add panko, grated zucchini, chopped garlic, half of the chives and Parmesan, 1 tablespoon of the harissa spice, 1 large egg, and ½ teaspoon salt; stir to combine. Form mixture into 4 (4-inch) fritters.
Make chive mayo: In a small bowl, stir together mayo and remaining chives. Season to taste with salt and a few generous grinds of pepper.
Fry fritters: Place ¼ cup flour on a plate, then gently dredge both sides of each fritter in flour, tapping off any excess. Heat ⅛ inch oil in a large skillet over medium-high until shimmering (oil should sizzle vigorously when a pinch of flour is added). Add fritters and cook until golden-brown, 3–4 minutes per side. Transfer to a paper towel-lined plate; sprinkle with salt.
Make salad & serve: In a medium bowl, stir together 1 tablespoon vinegar and 2 tablespoons oil. Add arugula, roasted tomatoes, and remaining Parmesan, and gently toss to combine. Season to taste with salt and pepper. Serve fritters over tomato-arugula salad with chive mayo spread over top or on the side for dipping.