In a small bowl, whisk yeast, water and 1 teaspoon sugar until yeast is dissolved. Let stand 5-10 minutes until yeast is foamy.
In a large mixing bowl or in the bowl of a stand mixer, add 2 ½ cups of bread flour. Make a well in center; add yeast mixture, remaining 1 tablespoon sugar, basil, Parmesan cheese, tomato soup, 2 tablespoons tomato paste, olive oil and salt. Stir with a wooden spoon or dough hook on low speed until just combined. Stir the remaining flour until dough forms.
On a well-floured surface or in bowl of a stand mixer with dough hook on medium speed, knead dough until smooth and elastic (about 10 minutes by hand, 5 minutes in stand mixer).
Shape dough into a ball; place in a large, lightly greased bowl. Turn to coat. Cover bowl with plastic wrap and let rise in warm place for 1 hour or until doubled.
Turn dough out onto a lightly floured countertop. Fold each of the four corners into the center, then flip the dough back over, seam-side down. Using both hands to cup the dough and pull it towards you, tighten the dough into a ball.
Place on a lightly greased rimmed cookie sheet. Cover with a kitchen towel and let rise 45 minutes to 1 hour or until doubled.
Meanwhile, pre-heat the oven to 375 degrees F. Using a sharp serrated knife, slice an X into top of loaf. Brush with cold water. Bake 30 minutes.
While the dough cooks, make the brown sugar glaze. In a small bowl, stir remaining 2 tablespoons tomato paste, brown sugar and 2 teaspoons of water until mixture is thick but brushable.
Remove the loaf from the oven after 30 minutes and brush the brown sugar glaze all over top of loaf using a pastry brush, silicone brush or a silicone spatula (not ideal!).
Return to oven to continue baking 5 to 10 minutes or until coating is mostly dried.
Cool loaf on a cooling rack 20 to 30 minutes before slicing.