To make the whipped feta, combine the feta, cream cheese, olive oil, lemon juice, lemon zest and garlic in a food processor. Blend until completely smooth and fluffy, about 2 minutes. Scrape down the sides as needed. Season with black pepper. Set aside.
For the tomato topping: in a large bowl, toss the halved Flavorbomb tomatoes with olive oil, lemon juice, minced garlic, and kosher salt. Let them sit for at least 10 minutes. They will release some of their juice and become even more flavorful. Fold in the chiffonade basil right before serving.
Grill the bread: brush both sides of each bread slice with olive oil. Grill over medium-high heat (or broil) in batches, 1 to 2 minutes per side, until golden and charred at the edges.
To assemble, spread each grilled bread slice with a generous layer of whipped feta. Spoon the marinated tomatoes over the top, including all of the juices. Finish with a drizzle of olive oil, a pinch of flaky sea salt, and za'atar if using. Serve immediately while bread is still warm.