For the holiday pizza dip: Preheat the oven to 450 degrees F. Line a rimmed baking sheet with aluminum foil.
Combine the tomatoes, oil, garlic, and oregano in a large bowl. Season with a big pinch of salt and the pepper. Spread the tomatoes in an even layer on the prepared baking sheet and cook until the tomatoes are slightly charred, 10 to 12 minutes.
Whip the cream cheese in the bowl of a stand mixer fitted with the paddle attachment. Stir in the ricotta, mozzarella and Parmesan until fully incorporated.
Stir in two-thirds of the roasted tomatoes and the red pepper flakes, then transfer to a 9-inch round baking dish. Bake until the top is golden brown, 15 to 18 minutes.
Scatter the remaining one-third of the roasted tomatoes on top and garnish with the basil.
For the pizza crackers: Divide the pizza dough into four pieces. Flour a square of parchment paper on a clean work surface. Place one piece of dough on the parchment paper and top with a second piece of parchment paper. Roll with a rolling pin until the dough is as thin as possible. Transfer the dough to a rimmed baking sheet, brush the top with olive oil lightly and sprinkle with the oregano, thyme and salt to taste. Repeat with the remaining pieces of dough.
Bake in two batches until golden brown, 6 to 7 minutes. Snap the pieces into irregular shapes and serve with the pizza dip.