In the bowl of an electric mixer, combine the water, yeast and sugar; stir to dissolve the sugar and yeast. Set aside until the yeast is bubbly and foamy, 10 to 15 minutes. Add the flour, 1 1/2 teaspoons of the salt and 3 tablespoons of the olive oil to the bowl. Using a dough hook, mix the flour and liquid on low speed until a dough comes together. Increase the speed to medium and allow the mixer to knead the dough for 5 minutes. Remove the dough from the bowl and place in a lightly greased bowl covered with a damp kitchen towel (or plastic wrap), to proof until doubled in size, about 2 hours.
Preheat the oven to 450 degrees F.
Punch the dough down and place on a lightly oiled 9 1/2-inch by 13-inch sheet pan. Cover with a damp kitchen towel or plastic wrap and allow to double in size again, about 30 to 45 minutes. Using your hands, press the dough so that it fits evenly across the entire pan. Spread the prosciutto strips evenly over the surface of the dough, then top with the sliced mozzarella. Sprinkle the chopped tomatoes over the top then drizzle with the remaining 6 tablespoons of olive oil. Sprinkle the top evenly with basil and the kosher salt and bake until golden brown, about 15 to 17 minutes. Rotate the focaccia half way through the cook time to ensure even browning.
Remove from the oven and allow to cool for at least 15 minutes before cutting and serving.