If using diced or whole tomatoes, use an immersion blender or food processor to process your tomatoes until they are the consistency of salsa.
In a large pot, over medium heat, heat oil. Add garlic and cook until lightly golden, 30 seconds to a minute. Carefully add tomatoes—oil will sizzle and pop as you do. Stir in sugar and basil. Bring mixture to a simmer.
Turn heat down as needed to keep at a good simmer and cover with a splatter screen if you have one. Simmer for 20 to 30 minutes, stirring occasionally, until sauce has thickened and reduced to about 1 1/2 cups. If you don’t own a splatter screen and the sauce is popping too aggressively, turn it down and extend the simmer time as necessary.
Add salt to taste.
Place naan loaves on baking sheets. Cover each with about 1/3 heaping cup of sauce. Top with 1/2 cup of cheese each and desired toppings.
Bake for 12 to 14 minutes, until cheese is melted and naan is golden. If baking all 4 pizzas at once, swap top and bottom trays once halfway through and keep an eye on the bottom tray to make sure the crust is not burning.
Cool on the baking sheet for 5 minutes before slicing, and enjoy!
*The salt content varies wildly between canned tomato brands, so you may need to add very little or quite a lot of salt depending on the brand you use.