In a large bowl, dissolve sugar and yeast in the warm water. Let sit for about 5 minutes.
Add 2 tbsp of olive oil and salt to the yeast mixture. Then, stir in the flour to form a dough.
Lightly oil a large bowl and place the dough in the bowl. Cover with a damp cloth and allow to rise in a warm place until the dough doubles in size (30-60 minutes).
Preheat oven to 425 degrees.
Deflate dough and place it on a lightly floured surface. Knead the dough briefly (about 30 seconds).
Place the dough on a greased baking sheet and pat into a large circle.
Press cherry tomatoes all over the dough and press them down lightly into the dough.
Brush dough with remaining 1 tbsp olive oil and sprinkle with course salt and rosemary.
Bake in preheated oven until golden brown, about 15 minutes.