Preheat the oven to 425°F. Place a pizza stone in the oven and let it preheat for at least one hour.
In a food processor, puree the tomatoes, red onion, 2 tablespoons of basil, 2 tablespoons of thyme, and garlic until smooth. Season the mixture with salt and pepper, to taste.
Melt 2 tablespoons of butter in a large pot over high heat. Add the tomato puree, tomato sauce, and tomato paste. Stir in brown sugar and simmer. Keep simmering until the mixture starts bubbling and thickens—this should take about 45 minutes to an hour. If necessary, adjust the temperature to prevent the sauce from burning.
Remove the sauce from the heat and let it cool until it's no longer steaming. While the sauce cools, combine all the pesto ingredients in a blender or food processor. Blend until smooth. Preserve any unused sauce for future pizzas!
In a small bowl, melt the remaining butter. Stir in garlic powder, onion powder, parsley, and salt. Unroll the pizza dough onto a pizza board or onto the preheated stone. Brush the garlic butter across the entire crust.
Spread a thin layer of pizza sauce over the dough. Slice the mozzarella cheese and arrange it on top of the pizza. Sprinkle any remaining basil leaves. Bake for 15-25 minutes, or until the pizza dough is cooked through and the mozzarella is bubbling.
Drizzle the pesto over the pizza as desired. Slice and serve hot right away. Enjoy!