Add the flour, sugar and salt to a food processor and pulse just until combined. In a small bowl, whisk mix together the egg, vinegar and water. Add the cold butter pieces into the food processor and pulse until small coarse crumbs remain. Sprinkle the water/egg mixture over the flour and pulse again until the dough comes together. Remove the dough with your hands and wrap it in plastic wrap. Refrigerate the dough for 30 minutes.
After 30 minutes, preheat the oven to 400 degrees F. Roll the dough out until it fits your tart pan (mine was a 10-inch springform pan) and press it into the pan. Poke holes in the crust with a fork. Bake the crust until golden and set, about 20 to 25 minutes. Allow the crust to cool to room temperature.
To make the feta, add crumbled feta to a food processor and pulse until small crumbs remain. Add in cream cheese and puree for 4-5 minutes, scraping down the sides when necessary, until feta is super creamy. Spread the feta inside of the crust. Top the feta with the sliced tomatoes, lots of salt and pepper and few fresh basil leaves. Cut into slices and serve immediately. You can refrigerate this overnight, but it’s definitely best served fresh. If you want to make it ahead, I suggest making the crust ahead, keeping the whipped feta in a bowl, and assembling right before serving.