Adjust oven rack to middle position and preheat oven to 400°F (204°C). Line a rimmed baking sheet with a double layer of paper towels or a clean kitchen towel.

In a colander set over a large bowl, toss the zucchini with salt and let drain for 30 minutes.

Press zucchini firmly with a rubber spatula to squeeze out moisture. Transfer zucchini to prepared baking sheet and spread evenly over towels; discard accumulated liquid and wipe out bowl. Blot zucchini with additional paper towels to remove excess moisture and set aside.

On a lightly floured surface, place one sheet of puff pastry directly on top of the other. Roll pastry into an 11- by 15-inch rectangle. Transfer pastry to prepared baking sheet and poke all over with a fork.

Cover with parchment and place another rimmed baking sheet on top. Bake until pastry is pale and firm to the touch, about 15 minutes. Remove top baking sheet and parchment. Increase oven temperature to 445°F (230°C).

In a medium bowl, combine cream cheese, Dijon mustard, thyme, and garlic (if using) and stir until well combined. Spread cream cheese mixture in an even layer over puff pastry, leaving a 1/2-inch border on all sides. Sprinkle evenly with mozzarella.

Add olive oil to bowl with reserved zucchini and toss to coat. Shingle zucchini in even rows over the mozzarella and season with freshly ground black pepper.

Bake tart until zucchini is tender and puff pastry is crisp and deeply browned at the edges, about 20 minutes.

Garnish tart with thyme leaves and lemon zest. Season with salt to taste. Cut into portions and serve immediately.