Preheat broiler to high. Line a large baking sheet with aluminum foil and spray foil with non-stick spray; set aside.
In a small bowl, mix all the cheese spread ingredients; set aside.
Divided pizza dough in half and roll out each into a 12 x 6-inch rectangle and place on prepared sheet. Brush each with half of the oil.
Broil for 3-4 minutes or until the dough is beginning to get brown. Flip dough and broil this side for the same amount of time. Remove and cool slightly on the baking sheet. Leave the broiler on.
Spread half the cheese spread on one dough rectangle and the remaining spread on the other dough rectangle.
Divide sliced tomatoes randomly on each rectangle. Sprinkle with the 2 tbs of grated cheese.
Place the flatbreads under the broiler and broil for about 5 minutes or until tomatoes begin to dry on top and cheese is beginning to brown.
Sprinkle with the basil and 1 tbs chopped parsley.
To prepare bread on the outside grill--grill each side of the bread over high heat about 3-4 minutes each side. Finish the flatbreads as per broiler instructions