For the vinaigrette: Roughly chop the tomatoes and mix with 2 teaspoons salt and the sugar. Let macerate for 10 minutes to get the juices running, and then use your hands to crush the tomatoes. Place the tomatoes in a fine mesh strainer set over a saucepot. Use a rubber spatula to press all the liquid out of the tomatoes. Discard the solids and save all the sweet juice.
Set the pot over medium heat and add the honey and garlic. Simmer for 10 minutes or so until you are left with about 1/2 cup worth of tomato juice.
Turn the heat off and add in the Dijon mustard. Then whisk in the olive oil to make an emulsification and season with salt and pepper.
For the salad: In a large bowl, add the greens and basil leaves. Pour over some of the vinaigrette to lightly coat the greens and gently toss. Shave some Parmesan over the top and finish with a few more cracks of fresh black pepper.