In a large bowl, stir the flour, salt, and sugar together.
Add the butter cubes and toss to cover with flour.
Cut in the butter with either a pastry blender or two knives until the butter is the size of peas, forming a coarse crumbly mixture.
Slowly add enough ice water, while mixing by hand.
Add water until the dough just starts to come together.
Bring it together into a ball, wrap in plastic and chill for at least one hour or even a day ahead.
In a medium-size pan, heat the olive oil over medium heat. Add the fennel and shallot slices. Lower the heat and cook until soften.
Remove from the pan and let them cool.
Preheat oven to 350°F.
While the fennel is cooling, roll out the dough to 1/8-inch thickness on a large piece of parchment paper.
Spread the cooled fennel mixture and basil over the dough.
Fold the edges over to create a border.
Sprinkle with the cheeses and cherry tomatoes. Add salt and pepper to taste over the tart.
Transfer the tart, with the parchment paper to a baking sheet.
Bake for 20 minutes or until the tart has browned. Serve warm.