In a large bowl or the bowl of your stand mixer, combine the flour and salt. In a one cup measuring cup, combine warm water, yeast and sugar. Let stand 5-10 minutes.
Add proofed yeast mixture and olive oil to bowl with flour and salt. Stir into a smooth dough, adding a few more tablespoons of flour, if necessary to make a smooth, moist (but not sticky) dough. Place into a greased bowl and cover with greased plastic wrap. Let rest/rise in a warm place for 1 hour.
Meanwhile, prepare the tomato sauce by combining all ingredients in a small bowl. Set aside.
Slice your tomatoes and bocconcini and place onto a doubled-up piece of paper towel to remove some of the moisture.
Pre-heat oven to 400° F. Prepare a large baking sheets with parchment paper and set aside. Have a second sheet of parchment paper ready.
Once oven is preheated, place tomato slices on the prepared baking sheet and pop into the oven for 10 minutes. Remove from oven (leaving oven on) and slide parchment with tomatoes onto a cooling rack. Place a fresh sheet of parchment onto the baking sheet and set aside.
When dough has rested, remove to a well-floured surface. Cut dough into 2 equal portions. Roll each portion on a floured surface to 1/4-inch thickness, about 5 inches wide and 12-14 inches long. Your flatbread can be any size or shape,d but oblong ones work really well as they'll fit side-by-side on a large baking sheet. Just be sure they aren't longer than the length of your baking sheet, so they don't hang over the edge.
Place two flatbreads side-by-side onto the prepared baking sheet. Divide the tomato sauce between the two flatbreads and using the back of a spoon, spread a thin layer over the flatbread, leaving the outside 3/4-inch uncovered. Let stand at room temperature for 10 - 15 minutes to rest.
Top flatbreads with roasted tomato slices. Sprinkle with salt and pepper.
Bake in preheated 400F oven for 15 minutes. Remove from oven and scatter with bocconcini slices. Return to oven for 2-3 minutes, or until bocconcini has just melted.
Remove from oven and allow to stand 5 minutes. Season with a bit more salt and pepper. Top with basil leaves and drizzle with balsamic glaze. Slice and serve warm.