Preheat the oven to 500 degrees F. Fit a rimmed baking sheet with a wire rack.
Add 4 inches vegetable oil to a large Dutch oven. Bring the oil to 375 degrees F.
On a lightly floured surface, shape the pizza dough into a 10- to 12-inch round (depending on the shape of your Dutch oven). Carefully drop the dough into the oil. (Always drop away from you!) Cook until the top is bubbly and the bottom is slightly golden, 2 to 3 minutes, then flip and cook another 1 to 2 minutes. Remove to the prepared rack.
Carefully press the dough down a bit for more surface area, and then top the fried pizza with the Mascarpone Bechamel, spreading it all around and leaving a thin border.
Drizzle the zucchini ribbons with the olive oil in a medium bowl and season with salt and pepper. Top the pizza with half of the shaved zucchini and the torn buffalo mozzarella. Bake until the cheese is melted, 5 to 7 minutes. Remove to a cutting board.
Meanwhile, toss the remaining zucchini ribbons with the lemon juice and torn basil. Top the warm pizza with the zucchini salad. Slice and eat up!
Melt the butter in a small saucepan over medium heat. Whisk in the flour and cook for 1 minute. Slowly whisk in the milk until smooth. Add the thyme sprigs and garlic and continue to simmer until the mixture thickens, 4 to 5 minutes. Season with salt. Remove the thyme sprigs and garlic. Whisk in the mascarpone. Set aside.