In a medium bowl, combine yeast, sugar, and warm water. Add 1 tablespoon flour, stir, and set aside for 30 minutes.
Sift the flour into a large bowl and add 3 tablespoons olive oil and the salt. Add the yeast liquid and mix into a soft, elastic dough. Knead for 5 minutes, until smooth. Cover the dough tightly with plastic wrap and refrigerate overnight (the dough can be refrigerated for up to 72 hours).
When ready to make the pizza, transfer the dough to a floured work surface. With floured hands, form the dough into a ball. Knead the dough by rolling it backwards and forwards, using your hands to stretch, pull, and push the dough. Keep kneading for 10 minutes, then cover with a towel and let sit to rise for 1 hour.
Preheat the oven to 450°F. Line a baking sheet with parchment paper and place in the oven to heat up.
When the dough has risen, roll it into a 10-inch diameter circle, around ¼-inch thick, and transfer to the baking sheet. Spread the tomato sauce over the pizza crust, dot with mozzarella, and top with tomatoes and ham slices.
Bake the pizza for 10 minutes, until the base is crisp and golden-brown around the edges and the mozzarella has melted.
Remove from the oven, scatter with fresh basil leaves, and serve.