Preheat the oven to 400°F (200°C). Line a rimmed baking sheet with parchment paper.
Unroll the one (9- to 11-oz) sheet puff pastry onto the prepared baking sheet.
Using a sharp knife, score a 3/4-inch (2 cm) border around the edge of the pastry, being careful to not cut all the way through. Prick the pastry inside the border all over with a fork. This will help to stop it from puffing up in the oven.
In a medium bowl, whisk together the 10 1/2 ounces whole milk ricotta, 1 clove garlic, 1 3/4 ounces (about 1/2 cup) Parmesan cheese, 1 tablespoon fresh basil, 2 tablespoons fresh chives1 tablespoon flat-leaf parsley, and the zest of 1 lemon (about 1 tablespoon), then season liberally.
Spread the ricotta mixture over the tart inside the border. Place the 5 ounces asparagus spears over the tart and dot around the 9 ounces cherry tomatoes, cut-side up. Gently press down on the tomatoes so that they sink slightly into the ricotta mixture, brush lightly with 1 tablespoon olive oil.
Brush the pastry border with the 1 large egg and bake until the pastry is golden and cooked through, 20 to 30 minutes. Season with sea salt and freshly ground black pepper and serve.