Pre-heat your oven to 400 degrees. Line a rimmed baking sheet with aluminum foil.
Spread the tomatoes on the prepared baking sheet. Drizzle with olive oil and balsamic and sprinkle with crushed red pepper and a pinch of kosher salt. Toss to coat.
Roast the tomatoes for 18-20 minutes until the tomatoes are soft and their skins are bursting. Let cool slightly.
Meanwhile, place the beans, basil, garlic, lemon juice and salt in the bowl of a food processor (or high-powered blender). Process until smooth, scraping down the bowl a few times if necessary. With the motor running, drizzle in the olive oil. Process for 30 seconds more until the spread becomes light and fluffy. Transfer to a bowl and briefly set aside.
Heat a grill or grill pan over medium-high heat. When hot, add the pitas and cook for 1-2 minutes per side until grill marks appear.
Spread each pita generously with the white bean basil spread. Top with roasted cherry tomatoes and sprinkle with Parmesan. Serve whole, or slice each pita into quarters with a sharp knife.